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

The derivative of ((-2x+4^7)/((3x-5)^5)) is -(2(-2x+4)^6(6x-5))/((3x-5)^6)

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

The first derivative of ((-2x+4^7)/((3x-5)^5)) is -(2(-2x+4)^6(6x-5))/((3x-5)^6)

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

- \frac{2 ( - 2 x + 4 ) ^{6} ( 6 x - 5 )}{( 3 x - 5 ) ^{6}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} ((- 2 x + 4)^{7}) = - 14 (- 2 x + 4)^{6}

\frac{d}{d x} ((3 x - 5)^{5}) = 15 (3 x - 5)^{4}

= \frac{( - 14 ( - 2 x + 4 ) ^{6} ) ( 3 x - 5 ) ^{5} - 15 ( 3 x - 5 ) ^{4} ( - 2 x + 4 ) ^{7}}{( ( 3 x - 5 ) ^{5} ) ^{2}}

Simplify

\frac{( - 14 ( - 2 x + 4 ) ^{6} ) ( 3 x - 5 ) ^{5} - 15 ( 3 x - 5 ) ^{4} ( - 2 x + 4 ) ^{7}}{( ( 3 x - 5 ) ^{5} ) ^{2}} : - \frac{2 ( - 2 x + 4 ) ^{6} ( 6 x - 5 )}{( 3 x - 5 ) ^{6}}

= - \frac{2 ( - 2 x + 4 ) ^{6} ( 6 x - 5 )}{( 3 x - 5 ) ^{6}}

ln (1 + x^{3})

\frac{d x}{d t} = x^{2} e^{- 2 t}, x (0) = 3

f (x) = \frac{1}{9 x}, at x = 9

\int cos (\frac{π}{x}) d x

f (x) = x (2 x + 2)

What is the derivative of ((-2x+4^7)/((3x-5)^5)) ?
The derivative of ((-2x+4^7)/((3x-5)^5)) is -(2(-2x+4)^6(6x-5))/((3x-5)^6)
What is the first derivative of ((-2x+4^7)/((3x-5)^5)) ?
The first derivative of ((-2x+4^7)/((3x-5)^5)) is -(2(-2x+4)^6(6x-5))/((3x-5)^6)