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 1/x^5
-
Derivative of x^5*cos(x)
-
Derivative of x^3*tan(x)
-
Derivative of x-3
-
Identical expressions
- e^(cos^ three *x^ seven)*arctg* seven *x^ five
- e to the power of ( co sinus of e of cubed multiply by x to the power of 7) multiply by arctg multiply by 7 multiply by x to the power of 5
- e to the power of ( co sinus of e of to the power of three multiply by x to the power of seven) multiply by arctg multiply by seven multiply by x to the power of five
- e(cos3*x7)*arctg*7*x5
- ecos3*x7*arctg*7*x5
- e^(cos³*x⁷)*arctg*7*x⁵
- e to the power of (cos to the power of 3*x to the power of 7)*arctg*7*x to the power of 5
- e^(cos^3x^7)arctg7x^5
- e(cos3x7)arctg7x5
- ecos3x7arctg7x5
- e^cos^3x^7arctg7x^5
Derivative of e^(cos^3*x^7)*arctg*7*x^5
The solution
You have entered
[src]
/ / 7\\ | \3 /| \(cos(x)) / 5 e *atan (7*x)
$$e^{\cos^{3^{7}}{\left(x \right)}} \operatorname{atan}^{5}{\left(7 x \right)}$$
/ / / 7\\ \ | | \3 /| | d | \(cos(x)) / 5 | --\e *atan (7*x)/ dx
$$\frac{d}{d x} e^{\cos^{3^{7}}{\left(x \right)}} \operatorname{atan}^{5}{\left(7 x \right)}$$
The first derivative
[src]
/ / 7\\ / / 7\\
| \3 /| / 7\ | \3 /|
4 \(cos(x)) / 5 \3 / \(cos(x)) /
35*atan (7*x)*e 2187*atan (7*x)*(cos(x)) *e *sin(x)
----------------------------- - ---------------------------------------------------
2 cos(x)
1 + 49*x
$$- \frac{2187 e^{\cos^{3^{7}}{\left(x \right)}} \sin{\left(x \right)} \cos^{3^{7}}{\left(x \right)} \operatorname{atan}^{5}{\left(7 x \right)}}{\cos{\left(x \right)}} + \frac{35 e^{\cos^{3^{7}}{\left(x \right)}} \operatorname{atan}^{4}{\left(7 x \right)}}{49 x^{2} + 1}$$
The second derivative
[src]
/ / 7\\
/ 2186 \ | \3 /|
3 | 490*(-2 + 7*x*atan(7*x)) 2 2185 / 2 2 2187 2 \ 153090*cos (x)*atan(7*x)*sin(x)| \(cos(x)) /
atan (7*x)*|- ------------------------ + 2187*atan (7*x)*cos (x)*\- cos (x) + 2186*sin (x) + 2187*cos (x)*sin (x)/ - ----------------------------------|*e
| 2 2 |
| / 2\ 1 + 49*x |
\ \1 + 49*x / /
$$\left(2187 \cdot \left(2187 \sin^{2}{\left(x \right)} \cos^{2187}{\left(x \right)} + 2186 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \cos^{2185}{\left(x \right)} \operatorname{atan}^{2}{\left(7 x \right)} - \frac{153090 \sin{\left(x \right)} \cos^{2186}{\left(x \right)} \operatorname{atan}{\left(7 x \right)}}{49 x^{2} + 1} - \frac{490 \cdot \left(7 x \operatorname{atan}{\left(7 x \right)} - 2\right)}{\left(49 x^{2} + 1\right)^{2}}\right) e^{\cos^{3^{7}}{\left(x \right)}} \operatorname{atan}^{3}{\left(7 x \right)}$$
The third derivative
[src]
/ / 2 2 \ \
| | 2 6 84*x*atan(7*x) 196*x *atan (7*x)| |
|3430*|- atan (7*x) + --------- - -------------- + -----------------| | / / 7\\
| | 2 2 2 | 2 2185 / 2 2 2187 2 \ 2186 | | \3 /|
2 | \ 1 + 49*x 1 + 49*x 1 + 49*x / 3 2184 / 2189 2 2 4374 2 2187 2 \ 229635*atan (7*x)*cos (x)*\- cos (x) + 2186*sin (x) + 2187*cos (x)*sin (x)/ 3214890*cos (x)*(-2 + 7*x*atan(7*x))*atan(7*x)*sin(x)| \(cos(x)) /
atan (7*x)*|-------------------------------------------------------------------- - 2187*atan (7*x)*cos (x)*\- 6561*cos (x) - 6559*cos (x) + 4776410*sin (x) + 4782969*cos (x)*sin (x) + 14342346*cos (x)*sin (x)/*sin(x) + --------------------------------------------------------------------------------- + --------------------------------------------------------|*e
| 2 2 2 |
| / 2\ 1 + 49*x / 2\ |
\ \1 + 49*x / \1 + 49*x / /
$$\left(- 2187 \cdot \left(4782969 \sin^{2}{\left(x \right)} \cos^{4374}{\left(x \right)} + 14342346 \sin^{2}{\left(x \right)} \cos^{2187}{\left(x \right)} + 4776410 \sin^{2}{\left(x \right)} - 6561 \cos^{2189}{\left(x \right)} - 6559 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} \cos^{2184}{\left(x \right)} \operatorname{atan}^{3}{\left(7 x \right)} + \frac{229635 \cdot \left(2187 \sin^{2}{\left(x \right)} \cos^{2187}{\left(x \right)} + 2186 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \cos^{2185}{\left(x \right)} \operatorname{atan}^{2}{\left(7 x \right)}}{49 x^{2} + 1} + \frac{3214890 \cdot \left(7 x \operatorname{atan}{\left(7 x \right)} - 2\right) \sin{\left(x \right)} \cos^{2186}{\left(x \right)} \operatorname{atan}{\left(7 x \right)}}{\left(49 x^{2} + 1\right)^{2}} + \frac{3430 \cdot \left(\frac{196 x^{2} \operatorname{atan}^{2}{\left(7 x \right)}}{49 x^{2} + 1} - \frac{84 x \operatorname{atan}{\left(7 x \right)}}{49 x^{2} + 1} - \operatorname{atan}^{2}{\left(7 x \right)} + \frac{6}{49 x^{2} + 1}\right)}{\left(49 x^{2} + 1\right)^{2}}\right) e^{\cos^{3^{7}}{\left(x \right)}} \operatorname{atan}^{2}{\left(7 x \right)}$$
The graph