Explore a world of knowledge and get your questions answered on IDNLearn.com. Discover reliable and timely information on any topic from our network of experienced professionals.

Use the General Power Rule to find the derivative of the function.y = (5x3 +2)2y' =

Use The General Power Rule To Find The Derivative Of The Functiony 5x3 22y class=

Sagot :

[tex]y=(5x^3+2)\placeholder{⬚}^2[/tex]

General power rule:

[tex]\frac{d}{dx}u^n=nu^{n-1}[/tex]

1. Use the change rule as follow:

[tex]\begin{gathered} u=5x^3+2 \\ \\ y^{\prime}=\frac{d}{du}u^2*\frac{d}{dx}(5x^3+2) \\ \\ y^{\prime}=\frac{d}{du}u^2*(\frac{d}{dx}5x^3+\frac{d}{dx}2) \end{gathered}[/tex]

2. Use the general power rule:

[tex]\begin{gathered} y^{\prime}=2u(15x^2+0) \\ \\ y^{\prime}=2u(15x^2) \end{gathered}[/tex]

3. Substitute u by its value and simplify:

[tex]\begin{gathered} y^{\prime}=2(5x^3+2)(15x^2) \\ y^{\prime}=30x^2(5x^3+2) \\ y^{\prime}=150x^5+60x^2 \end{gathered}[/tex]

Then, the derivate of the given function is:

[tex]y^{\prime}=150x^5+60x^2[/tex]