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

The derivative of (t^2+e^t)sqrt(t) is (5t^2+2e^tt+e^t)/(2sqrt(t))

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

The first derivative of (t^2+e^t)sqrt(t) is (5t^2+2e^tt+e^t)/(2sqrt(t))

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derivative of

(t^{2} + e^{t}) t

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d t} (t) = \frac{1}{2 t}

= (2 t + e^{t}) t + \frac{1}{2 t} (t^{2} + e^{t})

Simplify

(2 t + e^{t}) t + \frac{1}{2 t} (t^{2} + e^{t}) : \frac{5 t ^{2} + 2 e ^{t} t + e ^{t}}{2 t}

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

\frac{d}{d x} (cos^{2} (x) tan (x))

\frac{d}{d x} (cot (x) d x)

\int \frac{1}{x ( 2 x + 3 )} d x

\int 1 + \frac{1}{3 x} \frac{1}{x ^{2}} d x

\int \frac{8 + u}{u} d u

What is the derivative of (t^2+e^t)sqrt(t) ?
The derivative of (t^2+e^t)sqrt(t) is (5t^2+2e^tt+e^t)/(2sqrt(t))
What is the first derivative of (t^2+e^t)sqrt(t) ?
The first derivative of (t^2+e^t)sqrt(t) is (5t^2+2e^tt+e^t)/(2sqrt(t))