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Popular Calculus >

derivative of y=\sqrt[3]{1+7x}

Solution

derivative of

y = 3 1 + 7 x

Solution

\frac{7}{3 ( 1 + 7 x ) ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} (3 1 + 7 x)

Apply the chain rule:

\frac{1}{3 ( 1 + 7 x ) ^{\frac{2}{3}}} \frac{d}{d x} (1 + 7 x)

= \frac{1}{3 ( 1 + 7 x ) ^{\frac{2}{3}}} \frac{d}{d x} (1 + 7 x)

\frac{d}{d x} (1 + 7 x) = 7

= \frac{1}{3 ( 1 + 7 x ) ^{\frac{2}{3}}} \cdot 7

Simplify

\frac{1}{3 ( 1 + 7 x ) ^{\frac{2}{3}}} \cdot 7 : \frac{7}{3 ( 1 + 7 x ) ^{\frac{2}{3}}}

= \frac{7}{3 ( 1 + 7 x ) ^{\frac{2}{3}}}

Graph

Popular Examples

derivative of 18x^2

\frac{d}{d x} (18 x^{2})

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

integral from 1 to 4 of x^2+1/(4x^2)

\int_{1}^{4} x^{2} + \frac{1}{4 x ^{2}} d x

integral of (e^x)/(a+be^x)

\int \frac{e ^{x}}{a + b e ^{x}} d x

(3+x^2)y^'-2xy=0

(3 + x^{2}) y^{^{'}} - 2 x y = 0

Frequently Asked Questions (FAQ)

What is the derivative of y=\sqrt[3]{1+7x} ?
The derivative of y=\sqrt[3]{1+7x} is 7/(3(1+7x)^{2/3)}
What is the first derivative of y=\sqrt[3]{1+7x} ?
The first derivative of y=\sqrt[3]{1+7x} is 7/(3(1+7x)^{2/3)}