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

The derivative of t^2*sqrt(t^3+2) is (7t^4+8t)/(2sqrt(t^3+2))

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

The first derivative of t^2*sqrt(t^3+2) is (7t^4+8t)/(2sqrt(t^3+2))

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derivative of

t^{2} \cdot t^{3} + 2

\frac{7 t ^{4} + 8 t}{2 t ^{3} + 2}

Solution steps

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

Apply the Product Rule:

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

f = t^{2}, g = t^{3} + 2

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

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

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

= 2 t t^{3} + 2 + \frac{3 t ^{2}}{2 t ^{3} + 2} t^{2}

Simplify

2 t t^{3} + 2 + \frac{3 t ^{2}}{2 t ^{3} + 2} t^{2} : \frac{7 t ^{4} + 8 t}{2 t ^{3} + 2}

= \frac{7 t ^{4} + 8 t}{2 t ^{3} + 2}

\frac{1}{2 r} + \frac{1}{9 r ^{\frac{8}{9}}}

\frac{d}{d x} (\frac{7}{1 + x})

n = 1 \sum \infty \frac{4}{n ^{2} + 1}

\int - 9.8 d x

\int 2 e^{- 0.2 x} d x

What is the derivative of t^2*sqrt(t^3+2) ?
The derivative of t^2*sqrt(t^3+2) is (7t^4+8t)/(2sqrt(t^3+2))
What is the first derivative of t^2*sqrt(t^3+2) ?
The first derivative of t^2*sqrt(t^3+2) is (7t^4+8t)/(2sqrt(t^3+2))