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Popular >

derivative of (1-4x)/(2+x)

Solution

derivative of

\frac{1 - 4 x}{2 + x}

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{( - 4 ) ( 2 + x ) - 1 \cdot ( 1 - 4 x )}{( 2 + x ) ^{2}} : - \frac{9}{( 2 + x ) ^{2}}

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

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\int_{0}^{1} π (2 x)^{2} d x

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(9y^2-t^2)/(y^5)(dy)/(dt)+t/(2y^4)=0

\frac{9 y ^{2} - t ^{2}}{y ^{5}} \frac{d y}{d t} + \frac{t}{2 y ^{4}} = 0

(dy)/(dx)-y=e^x*y^2

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integral from 4 to infinity of 5e^{-y/2}

\int_{4}^{\infty} 5 e^{- \frac{y}{2}} d y

Frequently Asked Questions (FAQ)

What is the derivative of (1-4x)/(2+x) ?
The derivative of (1-4x)/(2+x) is -9/((2+x)^2)
What is the first derivative of (1-4x)/(2+x) ?
The first derivative of (1-4x)/(2+x) is -9/((2+x)^2)