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 sin(x)^2
-
Derivative of cos(x/3)
-
Derivative of √x
-
Derivative of 5x-1
-
Identical expressions
- three / four *ln(x^ two - two x+ three / two)+sqrt(two)/ two *arctg(sqrt(2)*(x- one))
- 3 divide by 4 multiply by ln(x squared minus 2x plus 3 divide by 2) plus square root of (2) divide by 2 multiply by arctg( square root of (2) multiply by (x minus 1))
- three divide by four multiply by ln(x to the power of two minus two x plus three divide by two) plus square root of (two) divide by two multiply by arctg( square root of (2) multiply by (x minus one))
- 3/4*ln(x^2-2x+3/2)+√(2)/2*arctg(√(2)*(x-1))
- 3/4*ln(x2-2x+3/2)+sqrt(2)/2*arctg(sqrt(2)*(x-1))
- 3/4*lnx2-2x+3/2+sqrt2/2*arctgsqrt2*x-1
- 3/4*ln(x²-2x+3/2)+sqrt(2)/2*arctg(sqrt(2)*(x-1))
- 3/4*ln(x to the power of 2-2x+3/2)+sqrt(2)/2*arctg(sqrt(2)*(x-1))
- 3/4ln(x^2-2x+3/2)+sqrt(2)/2arctg(sqrt(2)(x-1))
- 3/4ln(x2-2x+3/2)+sqrt(2)/2arctg(sqrt(2)(x-1))
- 3/4lnx2-2x+3/2+sqrt2/2arctgsqrt2x-1
- 3/4lnx^2-2x+3/2+sqrt2/2arctgsqrt2x-1
- 3 divide by 4*ln(x^2-2x+3 divide by 2)+sqrt(2) divide by 2*arctg(sqrt(2)*(x-1))
-
Similar expressions
- 3/4*ln(x^2-2x+3/2)+sqrt(2)/2*arctg(sqrt(2)*(x+1))
- 3/4*ln(x^2-2x-3/2)+sqrt(2)/2*arctg(sqrt(2)*(x-1))
- 3/4*ln(x^2-2x+3/2)-sqrt(2)/2*arctg(sqrt(2)*(x-1))
- 3/4*ln(x^2+2x+3/2)+sqrt(2)/2*arctg(sqrt(2)*(x-1))
Derivative of 3/4*ln(x^2-2x+3/2)+sqrt(2)/2*arctg(sqrt(2)*(x-1))
The solution
You have entered
[src]
/ 2 3\
3*log|x - 2*x + -| ___
\ 2/ \/ 2 / ___ \
------------------- + -----*atan\\/ 2 *(x - 1)/
4 2
$$\frac{3 \log{\left(\left(x^{2} - 2 x\right) + \frac{3}{2} \right)}}{4} + \frac{\sqrt{2}}{2} \operatorname{atan}{\left(\sqrt{2} \left(x - 1\right) \right)}$$
3*log(x^2 - 2*x + 3/2)/4 + (sqrt(2)/2)*atan(sqrt(2)*(x - 1))
The first derivative
[src]
1 3*(-2 + 2*x)
-------------- + ----------------
2 / 2 3\
1 + 2*(x - 1) 4*|x - 2*x + -|
\ 2/
$$\frac{3 \left(2 x - 2\right)}{4 \left(\left(x^{2} - 2 x\right) + \frac{3}{2}\right)} + \frac{1}{2 \left(x - 1\right)^{2} + 1}$$
The second derivative
[src]
2
3 12*(-1 + x) 4*(-1 + x)
-------------- - ----------------- - ------------------
2 2 2
3 - 4*x + 2*x / 2\ / 2\
\3 - 4*x + 2*x / \1 + 2*(-1 + x) /
$$- \frac{12 \left(x - 1\right)^{2}}{\left(2 x^{2} - 4 x + 3\right)^{2}} - \frac{4 \left(x - 1\right)}{\left(2 \left(x - 1\right)^{2} + 1\right)^{2}} + \frac{3}{2 x^{2} - 4 x + 3}$$
The third derivative
[src]
/ 2 3 \ | 1 9*(-1 + x) 8*(-1 + x) 24*(-1 + x) | 4*|- ------------------ - ----------------- + ------------------ + -----------------| | 2 2 3 3| | / 2\ / 2\ / 2\ / 2\ | \ \1 + 2*(-1 + x) / \3 - 4*x + 2*x / \1 + 2*(-1 + x) / \3 - 4*x + 2*x / /
$$4 \left(\frac{24 \left(x - 1\right)^{3}}{\left(2 x^{2} - 4 x + 3\right)^{3}} + \frac{8 \left(x - 1\right)^{2}}{\left(2 \left(x - 1\right)^{2} + 1\right)^{3}} - \frac{9 \left(x - 1\right)}{\left(2 x^{2} - 4 x + 3\right)^{2}} - \frac{1}{\left(2 \left(x - 1\right)^{2} + 1\right)^{2}}\right)$$