Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of e^(sin(1-3*x)^(2))
Derivative of 3*x^2+sin(x)
Derivative of (2x+5)/(3x-2)
Derivative of 12x-ln(12x)+4
Identical expressions
(3x^ two - five)^ four
(3x squared minus 5) to the power of 4
(3x to the power of two minus five) to the power of four
(3x2-5)4
3x2-54
(3x²-5)⁴
(3x to the power of 2-5) to the power of 4
3x^2-5^4
Similar expressions
(3x^2+5)^4

The derivative of the function/ (3x^2-5)^4

Derivative of (3x^2-5)^4

The solution

You have entered [src]

          4
/   2    \ 
\3*x  - 5/

$$\left(3 x^{2} - 5\right)^{4}$$

(3*x^2 - 5)^4

Detail solution

Let $u = 3 x^{2} - 5$ .
Apply the power rule: $u^{4}$ goes to $4 u^{3}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(3 x^{2} - 5\right)$ :
1. Differentiate $3 x^{2} - 5$ term by term:
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x^{2}$ goes to $2 x$
    So, the result is: $6 x$
  2. The derivative of the constant $-5$ is zero.
  The result is: $6 x$
The result of the chain rule is:

$24 x \left(3 x^{2} - 5\right)^{3}$
Now simplify:

$24 x \left(3 x^{2} - 5\right)^{3}$

The answer is:

$24 x \left(3 x^{2} - 5\right)^{3}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

               3
     /   2    \ 
24*x*\3*x  - 5/

$$24 x \left(3 x^{2} - 5\right)^{3}$$

Simplify

The second derivative [src]

              2             
   /        2\  /         2\
24*\-5 + 3*x / *\-5 + 21*x /

$$24 \left(3 x^{2} - 5\right)^{2} \left(21 x^{2} - 5\right)$$

Simplify

The third derivative [src]

       /        2\ /        2\
1296*x*\-5 + 3*x /*\-5 + 7*x /

$$1296 x \left(3 x^{2} - 5\right) \left(7 x^{2} - 5\right)$$

Simplify

The graph

Derivative of (3x^2-5)^4