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Popular >

derivative of (x^2-9^{2/3})

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (x^{2} - 9) = 2 x

= \frac{2}{3 ( x ^{2} - 9 ) ^{\frac{1}{3}}} \cdot 2 x

Simplify

\frac{2}{3 ( x ^{2} - 9 ) ^{\frac{1}{3}}} \cdot 2 x : \frac{4 x}{3 ( x ^{2} - 9 ) ^{\frac{1}{3}}}

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

Popular Examples

integral of (3x^2+2x-3)

\int (3 x^{2} + 2 x - 3) d x

sum from n=1 to infinity of 9/((n+1)!)

n = 1 \sum \infty \frac{9}{( n + 1 ) !}

tangent of f(x)=8x^2,\at x=10 tangent of

f (x) = 8 x^{2}, at x = 10

integral of (sqrt(5-x^2))/(x^2)

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

integral of 1+tan^2(x)-2cos(x)

\int 1 + tan^{2} (x) - 2 cos (x) d x

Frequently Asked Questions (FAQ)

What is the derivative of (x^2-9^{2/3}) ?
The derivative of (x^2-9^{2/3}) is (4x)/(3(x^2-9)^{1/3)}
What is the first derivative of (x^2-9^{2/3}) ?
The first derivative of (x^2-9^{2/3}) is (4x)/(3(x^2-9)^{1/3)}