Mister Exam

Other calculators


x^3*tan(x)

Derivative of x^3*tan(x)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 3       
x *tan(x)
$$x^{3} \tan{\left(x \right)}$$
d / 3       \
--\x *tan(x)/
dx           
$$\frac{d}{d x} x^{3} \tan{\left(x \right)}$$
Detail solution
  1. Apply the product rule:

    ; to find :

    1. Apply the power rule: goes to

    ; to find :

    1. Rewrite the function to be differentiated:

    2. Apply the quotient rule, which is:

      and .

      To find :

      1. The derivative of sine is cosine:

      To find :

      1. The derivative of cosine is negative sine:

      Now plug in to the quotient rule:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
 3 /       2   \      2       
x *\1 + tan (x)/ + 3*x *tan(x)
$$x^{3} \left(\tan^{2}{\left(x \right)} + 1\right) + 3 x^{2} \tan{\left(x \right)}$$
The second derivative [src]
    /               /       2   \    2 /       2   \       \
2*x*\3*tan(x) + 3*x*\1 + tan (x)/ + x *\1 + tan (x)/*tan(x)/
$$2 x \left(x^{2} \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + 3 x \left(\tan^{2}{\left(x \right)} + 1\right) + 3 \tan{\left(x \right)}\right)$$
The third derivative [src]
  /               /       2   \    3 /       2   \ /         2   \      2 /       2   \       \
2*\3*tan(x) + 9*x*\1 + tan (x)/ + x *\1 + tan (x)/*\1 + 3*tan (x)/ + 9*x *\1 + tan (x)/*tan(x)/
$$2 \left(x^{3} \left(\tan^{2}{\left(x \right)} + 1\right) \left(3 \tan^{2}{\left(x \right)} + 1\right) + 9 x^{2} \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + 9 x \left(\tan^{2}{\left(x \right)} + 1\right) + 3 \tan{\left(x \right)}\right)$$
The graph
Derivative of x^3*tan(x)