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Popular >

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

Solution

derivative of

\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

integral of (x^2-4x-6)/(x^2-6x)

\int \frac{x ^{2} - 4 x - 6}{x ^{2} - 6 x} d x

integral from 3 to 7 of x/(sqrt(7+x^2))

\int_{3}^{7} \frac{x}{7 + x ^{2}} d x

derivative of (xln(x)/(e^x))

\frac{d}{d x} (\frac{x ln ( x )}{e ^{x}})

(\partial)/(\partial x)(x^{1/3}y^{1/3})

\frac{\partial}{\partial x} (x^{\frac{1}{3}} y^{\frac{1}{3}})

derivative of 1/3 tan^3(x/2-tan(x/2))

\frac{d}{d x} (\frac{1}{3} tan^{3} (\frac{x}{2}) - tan (\frac{x}{2}))

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)