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Derivative of:
Derivative of x*sqrt(x)
Derivative of x*2
Derivative of y=8x^4
Derivative of xex
Sum of series:
f(x)
Integral of d{x}:
f(x)
f(x)
Identical expressions
f(x)= two x^ three +5x^2
f(x) equally 2x cubed plus 5x squared
f(x) equally two x to the power of three plus 5x squared
f(x)=2x3+5x2
fx=2x3+5x2
f(x)=2x³+5x²
f(x)=2x to the power of 3+5x to the power of 2
fx=2x^3+5x^2
Similar expressions
f(x)=2x^3-5x^2

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

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

The solution

You have entered [src]

   3      2
2*x  + 5*x

$$2 x^{3} + 5 x^{2}$$

2*x^3 + 5*x^2

Detail solution

Differentiate $2 x^{3} + 5 x^{2}$ 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: $x^{3}$ goes to $3 x^{2}$
  So, the result is: $6 x^{2}$
2. 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: $10 x$
The result is: $6 x^{2} + 10 x$
Now simplify:

$2 x \left(3 x + 5\right)$

The answer is:

$2 x \left(3 x + 5\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   2       
6*x  + 10*x

$$6 x^{2} + 10 x$$

Simplify

The second derivative [src]

2*(5 + 6*x)

$$2 \left(6 x + 5\right)$$

Simplify

The third derivative [src]

$$12$$

Simplify