What is the derivative of (x^2+6/((2x-7)^7)) ?

The derivative of (x^2+6/((2x-7)^7)) is (2(-5x^2-7x-42))/((2x-7)^8)

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

The first derivative of (x^2+6/((2x-7)^7)) is (2(-5x^2-7x-42))/((2x-7)^8)

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

\frac{2 ( - 5 x ^{2} - 7 x - 42 )}{( 2 x - 7 ) ^{8}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x^{2} + 6) = 2 x

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

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

Simplify

\frac{2 x ( 2 x - 7 ) ^{7} - 14 ( 2 x - 7 ) ^{6} ( x ^{2} + 6 )}{( ( 2 x - 7 ) ^{7} ) ^{2}} : \frac{2 ( - 5 x ^{2} - 7 x - 42 )}{( 2 x - 7 ) ^{8}}

= \frac{2 ( - 5 x ^{2} - 7 x - 42 )}{( 2 x - 7 ) ^{8}}

x \to 0 lim (\frac{200 π}{x})

y = \frac{y + 5 x}{3 y - x}, (1, 2)

\frac{d}{d x} (e^{2 t a n (x)})

1 + t

\int (2 x + 3) e^{2 x} d x

What is the derivative of (x^2+6/((2x-7)^7)) ?
The derivative of (x^2+6/((2x-7)^7)) is (2(-5x^2-7x-42))/((2x-7)^8)
What is the first derivative of (x^2+6/((2x-7)^7)) ?
The first derivative of (x^2+6/((2x-7)^7)) is (2(-5x^2-7x-42))/((2x-7)^8)