What is the derivative of t^2(6t+5)^3 ?

The derivative of t^2(6t+5)^3 is 2t(6t+5)^3+18(6t+5)^2t^2

What is the first derivative of t^2(6t+5)^3 ?

The first derivative of t^2(6t+5)^3 is 2t(6t+5)^3+18(6t+5)^2t^2

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derivative of

t^{2} (6 t + 5)^{3}

2 t (6 t + 5)^{3} + 18 (6 t + 5)^{2} t^{2}

Solution steps

\frac{d}{d t} (t^{2} (6 t + 5)^{3})

Apply the Product Rule:

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

f = t^{2}, g = (6 t + 5)^{3}

= \frac{d}{d t} (t^{2}) (6 t + 5)^{3} + \frac{d}{d t} ((6 t + 5)^{3}) t^{2}

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

\frac{d}{d t} ((6 t + 5)^{3}) = 18 (6 t + 5)^{2}

= 2 t (6 t + 5)^{3} + 18 (6 t + 5)^{2} t^{2}

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

\int_{0}^{18} x 18 - x d x

\frac{1}{( s - 2 )}

\frac{d}{d x} (\frac{x}{x + 4})

What is the derivative of t^2(6t+5)^3 ?
The derivative of t^2(6t+5)^3 is 2t(6t+5)^3+18(6t+5)^2t^2
What is the first derivative of t^2(6t+5)^3 ?
The first derivative of t^2(6t+5)^3 is 2t(6t+5)^3+18(6t+5)^2t^2