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Popular >

derivative of (4+x/(1-4x))

Solution

\frac{d}{d x} (\frac{4 + x}{1 - 4 x})

Solution

\frac{17}{( 1 - 4 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 + x}{1 - 4 x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 4 + x ) ( 1 - 4 x ) - \frac{d}{d x} ( 1 - 4 x ) ( 4 + x )}{( 1 - 4 x ) ^{2}}

\frac{d}{d x} (4 + x) = 1

\frac{d}{d x} (1 - 4 x) = - 4

= \frac{1 \cdot ( 1 - 4 x ) - ( - 4 ) ( 4 + x )}{( 1 - 4 x ) ^{2}}

Simplify

\frac{1 \cdot ( 1 - 4 x ) - ( - 4 ) ( 4 + x )}{( 1 - 4 x ) ^{2}} : \frac{17}{( 1 - 4 x ) ^{2}}

= \frac{17}{( 1 - 4 x ) ^{2}}

Popular Examples

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limit as x approaches 1 of e^{sqrt(x)}

x \to 1 lim (e^{x})

Frequently Asked Questions (FAQ)

What is the derivative of (4+x/(1-4x)) ?
The derivative of (4+x/(1-4x)) is (17)/((1-4x)^2)
What is the first derivative of (4+x/(1-4x)) ?
The first derivative of (4+x/(1-4x)) is (17)/((1-4x)^2)