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f(x)=(4x^2+5)^3

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Derivative of:
Derivative of f(x)=4x^2
Derivative of (sin(x))^2/cos(2*x)
Derivative of 6-6*x
Derivative of (5*x-x^2)/sqrt(x^2-1)
Sum of series:
f(x)
Integral of d{x}:
f(x)
f(x)
Identical expressions
f(x)=(4x^ two + five)^ three
f(x) equally (4x squared plus 5) cubed
f(x) equally (4x to the power of two plus five) to the power of three
f(x)=(4x2+5)3
fx=4x2+53
f(x)=(4x²+5)³
f(x)=(4x to the power of 2+5) to the power of 3
fx=4x^2+5^3
Similar expressions
f(x)=(4x^2-5)^3

The derivative of the function/ f(x)=(4x^2+5)^3

Derivative of f(x)=(4x^2+5)^3

The solution

You have entered [src]

          3
/   2    \ 
\4*x  + 5/

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

  /          3\
d |/   2    \ |
--\\4*x  + 5/ /
dx

$$\frac{d}{d x} \left(4 x^{2} + 5\right)^{3}$$

Transform

Detail solution

Let $u = 4 x^{2} + 5$ .
Apply the power rule: $u^{3}$ goes to $3 u^{2}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(4 x^{2} + 5\right)$ :
1. Differentiate $4 x^{2} + 5$ 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: $8 x$
  2. The derivative of the constant $5$ is zero.
  The result is: $8 x$
The result of the chain rule is:

$24 x \left(4 x^{2} + 5\right)^{2}$
Now simplify:

$24 x \left(4 x^{2} + 5\right)^{2}$

The answer is:

$24 x \left(4 x^{2} + 5\right)^{2}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

               2
     /   2    \ 
24*x*\4*x  + 5/

$$24 x \left(4 x^{2} + 5\right)^{2}$$

Simplify

The second derivative [src]

   /       2\ /        2\
24*\5 + 4*x /*\5 + 20*x /

$$24 \cdot \left(4 x^{2} + 5\right) \left(20 x^{2} + 5\right)$$

Simplify

The third derivative [src]

      /         2\
384*x*\15 + 20*x /

$$384 x \left(20 x^{2} + 15\right)$$

Simplify

The graph

Derivative of f(x)=(4x^2+5)^3