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Popular >

derivative of f(x)=(9x^6+2x^3)^4

Solution

derivative of

f (x) = (9 x^{6} + 2 x^{3})^{4}

Solution

4 (9 x^{6} + 2 x^{3})^{3} (54 x^{5} + 6 x^{2})

Solution steps

\frac{d}{d x} ((9 x^{6} + 2 x^{3})^{4})

Apply the chain rule:

4 (9 x^{6} + 2 x^{3})^{3} \frac{d}{d x} (9 x^{6} + 2 x^{3})

= 4 (9 x^{6} + 2 x^{3})^{3} \frac{d}{d x} (9 x^{6} + 2 x^{3})

\frac{d}{d x} (9 x^{6} + 2 x^{3}) = 54 x^{5} + 6 x^{2}

= 4 (9 x^{6} + 2 x^{3})^{3} (54 x^{5} + 6 x^{2})

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(9x^6+2x^3)^4 ?
The derivative of f(x)=(9x^6+2x^3)^4 is 4(9x^6+2x^3)^3(54x^5+6x^2)
What is the first derivative of f(x)=(9x^6+2x^3)^4 ?
The first derivative of f(x)=(9x^6+2x^3)^4 is 4(9x^6+2x^3)^3(54x^5+6x^2)