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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]

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