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Popular >

derivative of h(t)=(7t^2+t)^{-3}

Solution

derivative of

h (t) = (7 t^{2} + t)^{- 3}

Solution

- \frac{3 ( 14 t + 1 )}{( 7 t ^{2} + t ) ^{4}}

Solution steps

\frac{d}{d t} ((7 t^{2} + t)^{- 3})

Apply the chain rule:

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

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

\frac{d}{d t} (7 t^{2} + t) = 14 t + 1

= - \frac{3}{( 7 t ^{2} + t ) ^{4}} (14 t + 1)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{3 ( 14 t + 1 )}{( 7 t ^{2} + t ) ^{4}}

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Frequently Asked Questions (FAQ)

What is the derivative of h(t)=(7t^2+t)^{-3} ?
The derivative of h(t)=(7t^2+t)^{-3} is -(3(14t+1))/((7t^2+t)^4)
What is the first derivative of h(t)=(7t^2+t)^{-3} ?
The first derivative of h(t)=(7t^2+t)^{-3} is -(3(14t+1))/((7t^2+t)^4)