Mister Exam
Other calculators
- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
- Integral Step by Step
- Differential equations Step by Step
- Limits Step by Step
-
How to use it?
- Derivative of:
-
Derivative of e^(-x)
-
Derivative of sin(x)/cos(x)
-
Derivative of tanh(x)
-
Derivative of -e^x
-
Identical expressions
- three *x^ two / two - thirteen *x+ thirty-three *log(|x^ two + four *x+ five |)/ two -atan(x+ two)- thirty-three *log(five)/ two +atan(two)
- 3 multiply by x squared divide by 2 minus 13 multiply by x plus 33 multiply by logarithm of ( module of x squared plus 4 multiply by x plus 5|) divide by 2 minus arc tangent of gent of (x plus 2) minus 33 multiply by logarithm of (5) divide by 2 plus arc tangent of gent of (2)
- three multiply by x to the power of two divide by two minus thirteen multiply by x plus thirty minus three multiply by logarithm of ( module of x to the power of two plus four multiply by x plus five |) divide by two minus arc tangent of gent of (x plus two) minus thirty minus three multiply by logarithm of (five) divide by two plus arc tangent of gent of (two)
- 3*x2/2-13*x+33*log(|x2+4*x+5|)/2-atan(x+2)-33*log(5)/2+atan(2)
- 3*x2/2-13*x+33*log|x2+4*x+5|/2-atanx+2-33*log5/2+atan2
- 3*x²/2-13*x+33*log(|x²+4*x+5|)/2-atan(x+2)-33*log(5)/2+atan(2)
- 3*x to the power of 2/2-13*x+33*log(|x to the power of 2+4*x+5|)/2-atan(x+2)-33*log(5)/2+atan(2)
- 3x^2/2-13x+33log(|x^2+4x+5|)/2-atan(x+2)-33log(5)/2+atan(2)
- 3x2/2-13x+33log(|x2+4x+5|)/2-atan(x+2)-33log(5)/2+atan(2)
- 3x2/2-13x+33log|x2+4x+5|/2-atanx+2-33log5/2+atan2
- 3x^2/2-13x+33log|x^2+4x+5|/2-atanx+2-33log5/2+atan2
- 3*x^2 divide by 2-13*x+33*log(|x^2+4*x+5|) divide by 2-atan(x+2)-33*log(5) divide by 2+atan(2)
-
Similar expressions
- 3*x^2/2-13*x+33*log(|x^2-4*x+5|)/2-atan(x+2)-33*log(5)/2+atan(2)
- 3*x^2/2-13*x+33*log(|x^2+4*x-5|)/2-atan(x+2)-33*log(5)/2+atan(2)
- 3*x^2/2-13*x+33*log(|x^2+4*x+5|)/2-atan(x+2)+33*log(5)/2+atan(2)
- 3*x^2/2-13*x+33*log(|x^2+4*x+5|)/2+atan(x+2)-33*log(5)/2+atan(2)
- 3*x^2/2+13*x+33*log(|x^2+4*x+5|)/2-atan(x+2)-33*log(5)/2+atan(2)
- 3*x^2/2-13*x-33*log(|x^2+4*x+5|)/2-atan(x+2)-33*log(5)/2+atan(2)
- 3*x^2/2-13*x+33*log(|x^2+4*x+5|)/2-atan(x+2)-33*log(5)/2-atan(2)
- 3*x^2/2-13*x+33*log(|x^2+4*x+5|)/2-atan(x-2)-33*log(5)/2+atan(2)
- 3*x^2/2-13*x+33*log(|x^2+4*x+5|)/2-arctan(x+2)-33*log(5)/2+arctan(2)
Derivative of 3*x^2/2-13*x+33*log(|x^2+4*x+5|)/2-atan(x+2)-33*log(5)/2+atan(2)
The solution
You have entered
[src]
2 /| 2 |\ 3*x 33*log\|x + 4*x + 5|/ 33*log(5) ---- - 13*x + ---------------------- - atan(x + 2) - --------- + atan(2) 2 2 2
$$\left(\left(\left(\left(- 13 x + \frac{3 x^{2}}{2}\right) + \frac{33 \log{\left(\left|{\left(x^{2} + 4 x\right) + 5}\right| \right)}}{2}\right) - \operatorname{atan}{\left(x + 2 \right)}\right) - \frac{33 \log{\left(5 \right)}}{2}\right) + \operatorname{atan}{\left(2 \right)}$$
(3*x^2)/2 - 13*x + (33*log(|x^2 + 4*x + 5|))/2 - atan(x + 2) - 33*log(5)/2 + atan(2)
The first derivative
[src]
/ 2 \
1 33*(4 + 2*x)*sign\5 + x + 4*x/
-13 - ------------ + 3*x + -------------------------------
2 | 2 |
1 + (x + 2) 2*|x + 4*x + 5|
$$3 x + \frac{33 \left(2 x + 4\right) \operatorname{sign}{\left(x^{2} + 4 x + 5 \right)}}{2 \left|{\left(x^{2} + 4 x\right) + 5}\right|} - 13 - \frac{1}{\left(x + 2\right)^{2} + 1}$$
The second derivative
[src]
/ 2 \ 2 2/ 2 \ 2 / 2 \
2*(2 + x) 33*sign\5 + x + 4*x/ 66*(2 + x) *sign \5 + x + 4*x/ 132*(2 + x) *DiracDelta\5 + x + 4*x/
3 + --------------- + --------------------- - ------------------------------- + -------------------------------------
2 | 2 | 2 | 2 |
/ 2\ |5 + x + 4*x| / 2 \ |5 + x + 4*x|
\1 + (2 + x) / \5 + x + 4*x/
$$\frac{132 \left(x + 2\right)^{2} \delta\left(x^{2} + 4 x + 5\right)}{\left|{x^{2} + 4 x + 5}\right|} - \frac{66 \left(x + 2\right)^{2} \operatorname{sign}^{2}{\left(x^{2} + 4 x + 5 \right)}}{\left(x^{2} + 4 x + 5\right)^{2}} + \frac{2 \left(x + 2\right)}{\left(\left(x + 2\right)^{2} + 1\right)^{2}} + 3 + \frac{33 \operatorname{sign}{\left(x^{2} + 4 x + 5 \right)}}{\left|{x^{2} + 4 x + 5}\right|}$$
The third derivative
[src]
/ 2 2/ 2 \ 3 2/ 2 \ 3 / 2 \ / 2 \ 3 / 2 \ / 2 \\ | 1 4*(2 + x) 99*sign \5 + x + 4*x/*(2 + x) 132*(2 + x) *sign \5 + x + 4*x/ 132*(2 + x) *DiracDelta\5 + x + 4*x, 1/ 198*(2 + x)*DiracDelta\5 + x + 4*x/ 396*(2 + x) *DiracDelta\5 + x + 4*x/*sign\5 + x + 4*x/| 2*|--------------- - --------------- - ------------------------------ + -------------------------------- + ---------------------------------------- + ------------------------------------ - --------------------------------------------------------| | 2 3 2 3 | 2 | | 2 | 2 | |/ 2\ / 2\ / 2 \ / 2 \ |5 + x + 4*x| |5 + x + 4*x| / 2 \ | \\1 + (2 + x) / \1 + (2 + x) / \5 + x + 4*x/ \5 + x + 4*x/ \5 + x + 4*x/ /
$$2 \left(\frac{132 \left(x + 2\right)^{3} \delta^{\left( 1 \right)}\left( x^{2} + 4 x + 5 \right)}{\left|{x^{2} + 4 x + 5}\right|} - \frac{396 \left(x + 2\right)^{3} \delta\left(x^{2} + 4 x + 5\right) \operatorname{sign}{\left(x^{2} + 4 x + 5 \right)}}{\left(x^{2} + 4 x + 5\right)^{2}} + \frac{132 \left(x + 2\right)^{3} \operatorname{sign}^{2}{\left(x^{2} + 4 x + 5 \right)}}{\left(x^{2} + 4 x + 5\right)^{3}} - \frac{4 \left(x + 2\right)^{2}}{\left(\left(x + 2\right)^{2} + 1\right)^{3}} + \frac{198 \left(x + 2\right) \delta\left(x^{2} + 4 x + 5\right)}{\left|{x^{2} + 4 x + 5}\right|} - \frac{99 \left(x + 2\right) \operatorname{sign}^{2}{\left(x^{2} + 4 x + 5 \right)}}{\left(x^{2} + 4 x + 5\right)^{2}} + \frac{1}{\left(\left(x + 2\right)^{2} + 1\right)^{2}}\right)$$