Mister Exam

Other calculators


y=(2x+3)^5

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

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
         5
(2*x + 3) 
(2x+3)5\left(2 x + 3\right)^{5}
d /         5\
--\(2*x + 3) /
dx            
ddx(2x+3)5\frac{d}{d x} \left(2 x + 3\right)^{5}
Detail solution
  1. Let u=2x+3u = 2 x + 3.

  2. Apply the power rule: u5u^{5} goes to 5u45 u^{4}

  3. Then, apply the chain rule. Multiply by ddx(2x+3)\frac{d}{d x} \left(2 x + 3\right):

    1. Differentiate 2x+32 x + 3 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: xx goes to 11

        So, the result is: 22

      2. The derivative of the constant 33 is zero.

      The result is: 22

    The result of the chain rule is:

    10(2x+3)410 \left(2 x + 3\right)^{4}

  4. Now simplify:

    10(2x+3)410 \left(2 x + 3\right)^{4}


The answer is:

10(2x+3)410 \left(2 x + 3\right)^{4}

The graph
02468-8-6-4-2-1010-1000000010000000
The first derivative [src]
            4
10*(2*x + 3) 
10(2x+3)410 \left(2 x + 3\right)^{4}
The second derivative [src]
            3
80*(3 + 2*x) 
80(2x+3)380 \left(2 x + 3\right)^{3}
The third derivative [src]
             2
480*(3 + 2*x) 
480(2x+3)2480 \left(2 x + 3\right)^{2}
The graph
Derivative of y=(2x+3)^5