What is the derivative of y=(x^2+9)/((7x-1)^5) ?

The derivative of y=(x^2+9)/((7x-1)^5) is (-2x-21x^2-315)/((7x-1)^6)

What is the first derivative of y=(x^2+9)/((7x-1)^5) ?

The first derivative of y=(x^2+9)/((7x-1)^5) is (-2x-21x^2-315)/((7x-1)^6)

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derivative of

y = \frac{x ^{2} + 9}{( 7 x - 1 ) ^{5}}

\frac{- 2 x - 21 x ^{2} - 315}{( 7 x - 1 ) ^{6}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} + 9}{( 7 x - 1 ) ^{5}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} + 9 ) ( 7 x - 1 ) ^{5} - \frac{d}{d x} ( ( 7 x - 1 ) ^{5} ) ( x ^{2} + 9 )}{( ( 7 x - 1 ) ^{5} ) ^{2}}

\frac{d}{d x} (x^{2} + 9) = 2 x

\frac{d}{d x} ((7 x - 1)^{5}) = 35 (7 x - 1)^{4}

= \frac{2 x ( 7 x - 1 ) ^{5} - 35 ( 7 x - 1 ) ^{4} ( x ^{2} + 9 )}{( ( 7 x - 1 ) ^{5} ) ^{2}}

Simplify

\frac{2 x ( 7 x - 1 ) ^{5} - 35 ( 7 x - 1 ) ^{4} ( x ^{2} + 9 )}{( ( 7 x - 1 ) ^{5} ) ^{2}} : \frac{- 2 x - 21 x ^{2} - 315}{( 7 x - 1 ) ^{6}}

= \frac{- 2 x - 21 x ^{2} - 315}{( 7 x - 1 ) ^{6}}

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

n = 1 \sum \infty \frac{2 n}{5 n - 6}

(8 x^{2} + 9 x) e^{- 7 x}

\frac{d y}{d x} = x^{3} (1 - y), y (0) = 3

\int_{- \infty}^{- 8} x^{- \frac{4}{3}} d x

What is the derivative of y=(x^2+9)/((7x-1)^5) ?
The derivative of y=(x^2+9)/((7x-1)^5) is (-2x-21x^2-315)/((7x-1)^6)
What is the first derivative of y=(x^2+9)/((7x-1)^5) ?
The first derivative of y=(x^2+9)/((7x-1)^5) is (-2x-21x^2-315)/((7x-1)^6)