What is the derivative of g(t)=t^2sqrt(t) ?

The derivative of g(t)=t^2sqrt(t) is (5t^{3/2})/2

What is the first derivative of g(t)=t^2sqrt(t) ?

The first derivative of g(t)=t^2sqrt(t) is (5t^{3/2})/2

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derivative of

g (t) = t^{2} t

\frac{5 t ^{\frac{3}{2}}}{2}

Solution steps

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

Simplify

t^{2} t : t^{\frac{5}{2}}

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{5}{2} t^{\frac{5}{2} - 1}

Simplify

\frac{5}{2} t^{\frac{5}{2} - 1} : \frac{5 t ^{\frac{3}{2}}}{2}

= \frac{5 t ^{\frac{3}{2}}}{2}

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What is the derivative of g(t)=t^2sqrt(t) ?
The derivative of g(t)=t^2sqrt(t) is (5t^{3/2})/2
What is the first derivative of g(t)=t^2sqrt(t) ?
The first derivative of g(t)=t^2sqrt(t) is (5t^{3/2})/2