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Popular >

derivative of (2x+3/(5x+4))

Solution

\frac{d}{d x} (\frac{2 x + 3}{5 x + 4})

Solution

- \frac{7}{( 5 x + 4 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x + 3}{5 x + 4})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (2 x + 3) = 2

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

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

Simplify

\frac{2 ( 5 x + 4 ) - 5 ( 2 x + 3 )}{( 5 x + 4 ) ^{2}} : - \frac{7}{( 5 x + 4 ) ^{2}}

= - \frac{7}{( 5 x + 4 ) ^{2}}

Popular Examples

derivative of 2e^{(x-5})

\frac{d}{d x} (2 e^{(x - 5)})

integral of ((x^2+2))/(x+1)

\int \frac{( x ^{2} + 2 )}{x + 1} d x

derivative of (2x^2-3^3)

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

derivative of y= 2/((4x-3)^{1/2)}derivative of

y = \frac{2}{( 4 x - 3 ) ^{\frac{1}{2}}}

tangent of f(x)=(1+2x)^2 tangent of

f (x) = (1 + 2 x)^{2}

Frequently Asked Questions (FAQ)

What is the derivative of (2x+3/(5x+4)) ?
The derivative of (2x+3/(5x+4)) is -7/((5x+4)^2)
What is the first derivative of (2x+3/(5x+4)) ?
The first derivative of (2x+3/(5x+4)) is -7/((5x+4)^2)