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Popular >

derivative of \sqrt[3]{1+8x}

Solution

derivative of

Solution

\frac{8}{3 ( 1 + 8 x ) ^{\frac{2}{3}}}

Solution steps

Apply the chain rule:

\frac{1}{3 ( 1 + 8 x ) ^{\frac{2}{3}}} \frac{d}{d x} (1 + 8 x)

= \frac{1}{3 ( 1 + 8 x ) ^{\frac{2}{3}}} \frac{d}{d x} (1 + 8 x)

\frac{d}{d x} (1 + 8 x) = 8

= \frac{1}{3 ( 1 + 8 x ) ^{\frac{2}{3}}} \cdot 8

Simplify

\frac{1}{3 ( 1 + 8 x ) ^{\frac{2}{3}}} \cdot 8 : \frac{8}{3 ( 1 + 8 x ) ^{\frac{2}{3}}}

= \frac{8}{3 ( 1 + 8 x ) ^{\frac{2}{3}}}

Popular Examples

derivative of z/(z+d/z)derivative of

\frac{z}{z + \frac{d}{z}}

derivative of sqrt(ln(4x))derivative of

ln (4 x)

(\partial)/(\partial y)(2x-2xy)

\frac{\partial}{\partial y} (2 x - 2 x y)

f^'(x)=x^{1/3}(2x-1)(x+1)

f^{^{'}} (x) = x^{\frac{1}{3}} (2 x - 1) (x + 1)

tangent of f(x)=2sqrt(x)+1,\at x= 1/4 tangent of

f (x) = 2 x + 1, at x = \frac{1}{4}

Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[3]{1+8x} ?
The derivative of \sqrt[3]{1+8x} is 8/(3(1+8x)^{2/3)}
What is the first derivative of \sqrt[3]{1+8x} ?
The first derivative of \sqrt[3]{1+8x} is 8/(3(1+8x)^{2/3)}