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^(2-x)
-
Derivative of x^(4/5)
-
Derivative of f(x)=7
-
Derivative of (2*x-1)^2
-
Identical expressions
- arctane^cosx
- arc tangent of e to the power of co sinus of e of x
- arctanecosx
Derivative of arctane^cosx
The solution
You have entered
[src]
cos(x) atan (e)
$$\operatorname{atan}^{\cos{\left(x \right)}}{\left(e \right)}$$
d / cos(x) \ --\atan (e)/ dx
$$\frac{d}{d x} \operatorname{atan}^{\cos{\left(x \right)}}{\left(e \right)}$$
Detail solution
-
Let .
-
Then, apply the chain rule. Multiply by :
-
The derivative of cosine is negative sine:
The result of the chain rule is:
-
The answer is:
The first derivative
[src]
cos(x) -atan (e)*log(atan(e))*sin(x)
$$- \log{\left(\operatorname{atan}{\left(e \right)} \right)} \sin{\left(x \right)} \operatorname{atan}^{\cos{\left(x \right)}}{\left(e \right)}$$
The second derivative
[src]
cos(x) / 2 \ atan (e)*\-cos(x) + sin (x)*log(atan(e))/*log(atan(e))
$$\left(\log{\left(\operatorname{atan}{\left(e \right)} \right)} \sin^{2}{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(\operatorname{atan}{\left(e \right)} \right)} \operatorname{atan}^{\cos{\left(x \right)}}{\left(e \right)}$$
The third derivative
[src]
cos(x) / 2 2 \ atan (e)*\1 - log (atan(e))*sin (x) + 3*cos(x)*log(atan(e))/*log(atan(e))*sin(x)
$$\left(- \log{\left(\operatorname{atan}{\left(e \right)} \right)}^{2} \sin^{2}{\left(x \right)} + 3 \log{\left(\operatorname{atan}{\left(e \right)} \right)} \cos{\left(x \right)} + 1\right) \log{\left(\operatorname{atan}{\left(e \right)} \right)} \sin{\left(x \right)} \operatorname{atan}^{\cos{\left(x \right)}}{\left(e \right)}$$
The graph