What is the derivative of y= 1/((7x+12)^3) ?

The derivative of y= 1/((7x+12)^3) is -(21)/((7x+12)^4)

What is the first derivative of y= 1/((7x+12)^3) ?

The first derivative of y= 1/((7x+12)^3) is -(21)/((7x+12)^4)

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derivative of

y = \frac{1}{( 7 x + 12 ) ^{3}}

- \frac{21}{( 7 x + 12 ) ^{4}}

Solution steps

\frac{d}{d x} (\frac{1}{( 7 x + 12 ) ^{3}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} ((7 x + 12)^{- 3})

Apply the chain rule:

- \frac{3}{( 7 x + 12 ) ^{4}} \frac{d}{d x} (7 x + 12)

= - \frac{3}{( 7 x + 12 ) ^{4}} \frac{d}{d x} (7 x + 12)

\frac{d}{d x} (7 x + 12) = 7

= - \frac{3}{( 7 x + 12 ) ^{4}} \cdot 7

Simplify

- \frac{3}{( 7 x + 12 ) ^{4}} \cdot 7 : - \frac{21}{( 7 x + 12 ) ^{4}}

= - \frac{21}{( 7 x + 12 ) ^{4}}

\frac{d}{d x} (\frac{1}{3} x^{3} + x^{2} - x + 5)

n \to \infty lim (sin (\frac{nπ}{2}))

\int \frac{e ^{2 x}}{1 - e ^{2 x}} d x

x \to 3 - lim (\frac{x ^{2} - 9}{x - 3})

What is the derivative of y= 1/((7x+12)^3) ?
The derivative of y= 1/((7x+12)^3) is -(21)/((7x+12)^4)
What is the first derivative of y= 1/((7x+12)^3) ?
The first derivative of y= 1/((7x+12)^3) is -(21)/((7x+12)^4)