Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of (x^3)(4x+5)^4
Derivative of x^2-3*sin(x)
Derivative of x^2+2/x
Derivative of (x^2+1)^7
Identical expressions
(x^ two + one)^ seven
(x squared plus 1) to the power of 7
(x to the power of two plus one) to the power of seven
(x2+1)7
x2+17
(x²+1)⁷
(x to the power of 2+1) to the power of 7
x^2+1^7
Similar expressions
(x^2-1)^7

The derivative of the function/ (x^2+1)^7

Derivative of (x^2+1)^7

The solution

You have entered [src]

        7
/ 2    \ 
\x  + 1/

$$\left(x^{2} + 1\right)^{7}$$

(x^2 + 1)^7

Detail solution

Let $u = x^{2} + 1$ .
Apply the power rule: $u^{7}$ goes to $7 u^{6}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{2} + 1\right)$ :
1. Differentiate $x^{2} + 1$ term by term:
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  2. The derivative of the constant $1$ is zero.
  The result is: $2 x$
The result of the chain rule is:

$14 x \left(x^{2} + 1\right)^{6}$
Now simplify:

$14 x \left(x^{2} + 1\right)^{6}$

The answer is:

$14 x \left(x^{2} + 1\right)^{6}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

             6
     / 2    \ 
14*x*\x  + 1/

$$14 x \left(x^{2} + 1\right)^{6}$$

Simplify

The second derivative [src]

           5            
   /     2\  /        2\
14*\1 + x / *\1 + 13*x /

$$14 \left(x^{2} + 1\right)^{5} \left(13 x^{2} + 1\right)$$

Simplify

The third derivative [src]

              4            
      /     2\  /        2\
168*x*\1 + x / *\3 + 13*x /

$$168 x \left(x^{2} + 1\right)^{4} \left(13 x^{2} + 3\right)$$

Simplify

The graph

Derivative of (x^2+1)^7