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Popular Calculus >

derivative of (3x^6+4x^3)^4

Solution

derivative of

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

Solution

4 (3 x^{6} + 4 x^{3})^{3} (18 x^{5} + 12 x^{2})

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (3 x^{6} + 4 x^{3}) = 18 x^{5} + 12 x^{2}

= 4 (3 x^{6} + 4 x^{3})^{3} (18 x^{5} + 12 x^{2})

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (3x^6+4x^3)^4 ?
The derivative of (3x^6+4x^3)^4 is 4(3x^6+4x^3)^3(18x^5+12x^2)
What is the first derivative of (3x^6+4x^3)^4 ?
The first derivative of (3x^6+4x^3)^4 is 4(3x^6+4x^3)^3(18x^5+12x^2)