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

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

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

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

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derivative of

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}

x \to 0 + lim (x ln (x))

x \to 3 - lim (\frac{8}{x - 3})

x (\frac{d y}{d x}) - y = 3 x^{2}

\frac{d}{d x} (4 - x^{2} - 4 y^{2})

k = 1 \sum \infty e^{k}

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