What is the derivative of (3x^6+2x^3)^4 ?

The derivative of (3x^6+2x^3)^4 is 4(3x^6+2x^3)^3(18x^5+6x^2)

What is the first derivative of (3x^6+2x^3)^4 ?

The first derivative of (3x^6+2x^3)^4 is 4(3x^6+2x^3)^3(18x^5+6x^2)

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derivative of

(3 x^{6} + 2 x^{3})^{4}

4 (3 x^{6} + 2 x^{3})^{3} (18 x^{5} + 6 x^{2})

Solution steps

\frac{d}{d x} ((3 x^{6} + 2 x^{3})^{4})

Apply the chain rule:

4 (3 x^{6} + 2 x^{3})^{3} \frac{d}{d x} (3 x^{6} + 2 x^{3})

= 4 (3 x^{6} + 2 x^{3})^{3} \frac{d}{d x} (3 x^{6} + 2 x^{3})

\frac{d}{d x} (3 x^{6} + 2 x^{3}) = 18 x^{5} + 6 x^{2}

= 4 (3 x^{6} + 2 x^{3})^{3} (18 x^{5} + 6 x^{2})

\int \frac{( 16 x ^{2} )}{( 2 x + 5 ) ^{5}} d x

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What is the derivative of (3x^6+2x^3)^4 ?
The derivative of (3x^6+2x^3)^4 is 4(3x^6+2x^3)^3(18x^5+6x^2)
What is the first derivative of (3x^6+2x^3)^4 ?
The first derivative of (3x^6+2x^3)^4 is 4(3x^6+2x^3)^3(18x^5+6x^2)