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Popular >

derivative of (3+8x/(5-4x))

Solution

\frac{d}{d x} (\frac{3 + 8 x}{5 - 4 x})

Solution

\frac{52}{( 5 - 4 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 + 8 x}{5 - 4 x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 + 8 x ) ( 5 - 4 x ) - \frac{d}{d x} ( 5 - 4 x ) ( 3 + 8 x )}{( 5 - 4 x ) ^{2}}

\frac{d}{d x} (3 + 8 x) = 8

\frac{d}{d x} (5 - 4 x) = - 4

= \frac{8 ( 5 - 4 x ) - ( - 4 ) ( 3 + 8 x )}{( 5 - 4 x ) ^{2}}

Simplify

\frac{8 ( 5 - 4 x ) - ( - 4 ) ( 3 + 8 x )}{( 5 - 4 x ) ^{2}} : \frac{52}{( 5 - 4 x ) ^{2}}

= \frac{52}{( 5 - 4 x ) ^{2}}

Popular Examples

derivative of x^3-2x^2+2

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

(\partial)/(\partial y)(xcos(y)sin(z))

\frac{\partial}{\partial y} (x cos (y) sin (z))

2y^'+10y=80,y(0)=0

2 y^{^{'}} + 10 y = 80, y (0) = 0

(\partial)/(\partial x)(sqrt(8-2x^2-y^2))

\frac{\partial}{\partial x} (8 - 2 x^{2} - y^{2})

derivative of g(0)=(4-2x)e^n-4 derivative of

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Frequently Asked Questions (FAQ)

What is the derivative of (3+8x/(5-4x)) ?
The derivative of (3+8x/(5-4x)) is (52)/((5-4x)^2)
What is the first derivative of (3+8x/(5-4x)) ?
The first derivative of (3+8x/(5-4x)) is (52)/((5-4x)^2)