What is the derivative of t^2(5t+9)^3 ?

The derivative of t^2(5t+9)^3 is 2t(5t+9)^3+15(5t+9)^2t^2

What is the first derivative of t^2(5t+9)^3 ?

The first derivative of t^2(5t+9)^3 is 2t(5t+9)^3+15(5t+9)^2t^2

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derivative of

t^{2} (5 t + 9)^{3}

2 t (5 t + 9)^{3} + 15 (5 t + 9)^{2} t^{2}

Solution steps

\frac{d}{d t} (t^{2} (5 t + 9)^{3})

Apply the Product Rule:

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

f = t^{2}, g = (5 t + 9)^{3}

= \frac{d}{d t} (t^{2}) (5 t + 9)^{3} + \frac{d}{d t} ((5 t + 9)^{3}) t^{2}

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

\frac{d}{d t} ((5 t + 9)^{3}) = 15 (5 t + 9)^{2}

= 2 t (5 t + 9)^{3} + 15 (5 t + 9)^{2} t^{2}

2 x^{3} - 3 x^{2}

\frac{1}{x - 1}, 0

x \to 1 lim (\frac{sin ( x )}{x})

\frac{3}{( 1 - x ^{2} ) ^{4}}

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

What is the derivative of t^2(5t+9)^3 ?
The derivative of t^2(5t+9)^3 is 2t(5t+9)^3+15(5t+9)^2t^2
What is the first derivative of t^2(5t+9)^3 ?
The first derivative of t^2(5t+9)^3 is 2t(5t+9)^3+15(5t+9)^2t^2