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

The derivative of (3x+4/(7x-5)) is -(43)/((7x-5)^2)

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

The first derivative of (3x+4/(7x-5)) is -(43)/((7x-5)^2)

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\frac{d}{d x} (\frac{3 x + 4}{7 x - 5})

- \frac{43}{( 7 x - 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 x + 4}{7 x - 5})

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (7 x - 5) = 7

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

Simplify

\frac{3 ( 7 x - 5 ) - 7 ( 3 x + 4 )}{( 7 x - 5 ) ^{2}} : - \frac{43}{( 7 x - 5 ) ^{2}}

= - \frac{43}{( 7 x - 5 ) ^{2}}

(x^{2} - 24)^{6}

5 x^{2} + 2 x, at x = 3

\int sin^{3} (4 θ) cos (4 θ) d θ

f (x) = x^{2} + 4

\frac{d y}{d x} = \frac{1 + x y}{1 + x}

What is the derivative of (3x+4/(7x-5)) ?
The derivative of (3x+4/(7x-5)) is -(43)/((7x-5)^2)
What is the first derivative of (3x+4/(7x-5)) ?
The first derivative of (3x+4/(7x-5)) is -(43)/((7x-5)^2)