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Popular >

derivative of \sqrt[3]{9x^2+4}

Solution

Solution

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

Solution steps

Apply the chain rule:

\frac{1}{3 ( 9 x ^{2} + 4 ) ^{\frac{2}{3}}} \frac{d}{d x} (9 x^{2} + 4)

= \frac{1}{3 ( 9 x ^{2} + 4 ) ^{\frac{2}{3}}} \frac{d}{d x} (9 x^{2} + 4)

\frac{d}{d x} (9 x^{2} + 4) = 18 x

= \frac{1}{3 ( 9 x ^{2} + 4 ) ^{\frac{2}{3}}} \cdot 18 x

Simplify

\frac{1}{3 ( 9 x ^{2} + 4 ) ^{\frac{2}{3}}} \cdot 18 x : \frac{6 x}{( 9 x ^{2} + 4 ) ^{\frac{2}{3}}}

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

Popular Examples

derivative of x^2arcsinh(9x)

\frac{d}{d x} (x^{2} arcsinh (9 x))

integral of 1/(x^5)-3/(x^2)

\int \frac{1}{x ^{5}} - \frac{3}{x ^{2}} d x

xy^'+2y=x^2-x+1

x y^{^{'}} + 2 y = x^{2} - x + 1

tangent of f(x)=ln(x^2-9x+1),(9,0)tangent of

f (x) = ln (x^{2} - 9 x + 1), (9, 0)

slope of (-2,2),(1,-2)slope

(- 2, 2), (1, - 2)

Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[3]{9x^2+4} ?
The derivative of \sqrt[3]{9x^2+4} is (6x)/((9x^2+4)^{2/3)}
What is the first derivative of \sqrt[3]{9x^2+4} ?
The first derivative of \sqrt[3]{9x^2+4} is (6x)/((9x^2+4)^{2/3)}