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Popular >

derivative of h(t)=t^2(7t+8)^3

Solution

derivative of

h (t) = t^{2} (7 t + 8)^{3}

Solution

2 t (7 t + 8)^{3} + 21 (7 t + 8)^{2} t^{2}

Solution steps

\frac{d}{d t} (t^{2} (7 t + 8)^{3})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = t^{2}, g = (7 t + 8)^{3}

= \frac{d}{d t} (t^{2}) (7 t + 8)^{3} + \frac{d}{d t} ((7 t + 8)^{3}) t^{2}

\frac{d}{d t} (t^{2}) = 2 t

\frac{d}{d t} ((7 t + 8)^{3}) = 21 (7 t + 8)^{2}

= 2 t (7 t + 8)^{3} + 21 (7 t + 8)^{2} t^{2}

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Frequently Asked Questions (FAQ)

What is the derivative of h(t)=t^2(7t+8)^3 ?
The derivative of h(t)=t^2(7t+8)^3 is 2t(7t+8)^3+21(7t+8)^2t^2
What is the first derivative of h(t)=t^2(7t+8)^3 ?
The first derivative of h(t)=t^2(7t+8)^3 is 2t(7t+8)^3+21(7t+8)^2t^2