What is the derivative of t^2(5t+2)^3 ?

The derivative of t^2(5t+2)^3 is 2t(5t+2)^3+15(5t+2)^2t^2

What is the first derivative of t^2(5t+2)^3 ?

The first derivative of t^2(5t+2)^3 is 2t(5t+2)^3+15(5t+2)^2t^2

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derivative of

t^{2} (5 t + 2)^{3}

2 t (5 t + 2)^{3} + 15 (5 t + 2)^{2} t^{2}

Solution steps

\frac{d}{d t} (t^{2} (5 t + 2)^{3})

Apply the Product Rule:

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

f = t^{2}, g = (5 t + 2)^{3}

= \frac{d}{d t} (t^{2}) (5 t + 2)^{3} + \frac{d}{d t} ((5 t + 2)^{3}) t^{2}

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

\frac{d}{d t} ((5 t + 2)^{3}) = 15 (5 t + 2)^{2}

= 2 t (5 t + 2)^{3} + 15 (5 t + 2)^{2} t^{2}

\int e^{4 x - 7} d x

f (x) = cot^{2} (x)

\int e^{0.04 x} d x

y^{^{'}} + y = 2 e^{- t}

\int_{0}^{2} t e^{- 1} d t

What is the derivative of t^2(5t+2)^3 ?
The derivative of t^2(5t+2)^3 is 2t(5t+2)^3+15(5t+2)^2t^2
What is the first derivative of t^2(5t+2)^3 ?
The first derivative of t^2(5t+2)^3 is 2t(5t+2)^3+15(5t+2)^2t^2