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Popular >

derivative of \sqrt[3]{x^3-9x}

Solution

Solution

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

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

taylor sin(cos(x))taylor

sin (cos (x))

limit as x approaches 0-of e^{9/x}

x \to 0 - lim (e^{\frac{9}{x}})

limit as x approaches infinity of x*0

x \to \infty lim (x \cdot 0)

implicit (dy)/(dx),xy+4=x implicit derivative

\frac{d y}{d x}, x y + 4 = x

x^2(dy)/(dx)=y-xy,y(-1)=-6

x^{2} \frac{d y}{d x} = y - x y, y (- 1) = - 6

Frequently Asked Questions (FAQ)

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