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Popular >

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

Solution

derivative of

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

Solution

4 (9 x^{3} + 3 x^{2})^{3} (27 x^{2} + 6 x)

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (9 x^{3} + 3 x^{2}) = 27 x^{2} + 6 x

= 4 (9 x^{3} + 3 x^{2})^{3} (27 x^{2} + 6 x)

Popular Examples

derivative of sqrt(6+tan^2(x))

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

derivative of (18/(x^4))

\frac{d}{d x} (\frac{18}{x ^{4}})

integral of 1/(sec^2(u))

\int \frac{1}{sec ^{2} ( u )} d u

integral from 0 to 4 of |2x-3|

\int_{0}^{4} ∣ 2 x - 3 ∣ d x

inverse oflaplace s/(s+1/2)inverse laplace

\frac{s}{s + \frac{1}{2}}

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(9x^3+3x^2)^4 ?
The derivative of f(x)=(9x^3+3x^2)^4 is 4(9x^3+3x^2)^3(27x^2+6x)
What is the first derivative of f(x)=(9x^3+3x^2)^4 ?
The first derivative of f(x)=(9x^3+3x^2)^4 is 4(9x^3+3x^2)^3(27x^2+6x)