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Popular >

derivative of ln(\sqrt[7]{x})

Solution

\frac{d}{d x} (ln (7 x))

Solution

\frac{1}{7 7 x x ^{\frac{6}{7}}}

Solution steps

\frac{d}{d x} (ln (7 x))

Apply the chain rule:

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

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

\frac{d}{d x} (7 x) = \frac{1}{7 x ^{\frac{6}{7}}}

= \frac{1}{7 x} \cdot \frac{1}{7 x ^{\frac{6}{7}}}

Simplify

\frac{1}{7 x} \cdot \frac{1}{7 x ^{\frac{6}{7}}} : \frac{1}{7 7 x x ^{\frac{6}{7}}}

= \frac{1}{7 7 x x ^{\frac{6}{7}}}

Graph

Popular Examples

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\int \frac{( 2 x - 1 )}{( x - 1 ) ( x - 2 )} d x

(e^x)/(\frac{dy){dx}}=(1+e^x)y

\frac{e ^{x}}{\frac{d y}{d x}} = (1 + e^{x}) y

y^{''}-6y^'+25y=50t^3-36t^2-63t+18

y^{^{''}} - 6 y^{^{'}} + 25 y = 50 t^{3} - 36 t^{2} - 63 t + 18

(\partial)/(\partial x)(ln(t))

\frac{\partial}{\partial x} (ln (t))

Frequently Asked Questions (FAQ)

What is the derivative of ln(\sqrt[7]{x}) ?
The derivative of ln(\sqrt[7]{x}) is 1/(7\sqrt[7]{x)x^{6/7}}
What is the first derivative of ln(\sqrt[7]{x}) ?
The first derivative of ln(\sqrt[7]{x}) is 1/(7\sqrt[7]{x)x^{6/7}}