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Popular >

derivative of f(x)=(3x+4)/(2x+1)

Solution

derivative of

f (x) = \frac{3 x + 4}{2 x + 1}

Solution

- \frac{5}{( 2 x + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 x + 4}{2 x + 1})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (3 x + 4) = 3

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

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

Simplify

\frac{3 ( 2 x + 1 ) - 2 ( 3 x + 4 )}{( 2 x + 1 ) ^{2}} : - \frac{5}{( 2 x + 1 ) ^{2}}

= - \frac{5}{( 2 x + 1 ) ^{2}}

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z \to - 3 lim (\frac{z ^{2} - 9}{z + 3})

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\int sec^{6} (7 x) d x

y^'=0.0012y(1900-y)

y^{^{'}} = 0.0012 y (1900 - y)

(\partial)/(\partial x)(x^3+y^3+z^3-3xyz)

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(3x+4)/(2x+1) ?
The derivative of f(x)=(3x+4)/(2x+1) is -5/((2x+1)^2)
What is the first derivative of f(x)=(3x+4)/(2x+1) ?
The first derivative of f(x)=(3x+4)/(2x+1) is -5/((2x+1)^2)