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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derivative of

\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}}

a y^{^{'}} + b y = 0

4 t x \frac{d x}{d t} = x^{2} + 1

\frac{\partial}{\partial z} (cos (k z - wt))

\frac{1}{2 s ^{2} + s + 1}

x \to 1 lim ((3 x - 4)^{2})

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)