What is the derivative of f(t)=t^{5/3}e^t ?

The derivative of f(t)=t^{5/3}e^t is (5e^tt^{2/3})/3+e^tt^{5/3}

What is the first derivative of f(t)=t^{5/3}e^t ?

The first derivative of f(t)=t^{5/3}e^t is (5e^tt^{2/3})/3+e^tt^{5/3}

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derivative of

f (t) = t^{\frac{5}{3}} e^{t}

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

Solution steps

\frac{d}{d t} (t^{\frac{5}{3}} e^{t})

Apply the Product Rule:

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

f = t^{\frac{5}{3}}, g = e^{t}

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

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

\int_{0}^{\infty} e^{- x} cos (x) d x

\frac{\partial}{\partial x} (e^{- 2 t} cos (π x))

\frac{d y}{d t} = \frac{t}{y e ^{y + t^{2}}}

\frac{d}{d x} (sin^{4} (3 x) tan^{3} (4 x))

\int \frac{x ^{2}}{a ^{2} + ( x - b ) ^{2}} d x

What is the derivative of f(t)=t^{5/3}e^t ?
The derivative of f(t)=t^{5/3}e^t is (5e^tt^{2/3})/3+e^tt^{5/3}
What is the first derivative of f(t)=t^{5/3}e^t ?
The first derivative of f(t)=t^{5/3}e^t is (5e^tt^{2/3})/3+e^tt^{5/3}