What is the derivative of 2t+4/3 t^{3/2}+(t^2)/2 ?

The derivative of 2t+4/3 t^{3/2}+(t^2)/2 is 2+2t^{1/2}+t

What is the first derivative of 2t+4/3 t^{3/2}+(t^2)/2 ?

The first derivative of 2t+4/3 t^{3/2}+(t^2)/2 is 2+2t^{1/2}+t

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derivative of

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

2 + 2 t^{\frac{1}{2}} + t

Solution steps

\frac{d}{d t} (2 t + \frac{4}{3} t^{\frac{3}{2}} + \frac{t ^{2}}{2})

Simplify

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

= \frac{d}{d t} (2 t + \frac{4 t ^{\frac{3}{2}}}{3} + \frac{t ^{2}}{2})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d t} (2 t) + \frac{d}{d t} (\frac{4 t ^{\frac{3}{2}}}{3}) + \frac{d}{d t} (\frac{t ^{2}}{2})

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

\frac{d}{d t} (\frac{4 t ^{\frac{3}{2}}}{3}) = 2 t^{\frac{1}{2}}

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

= 2 + 2 t^{\frac{1}{2}} + t

\int_{0}^{2} \frac{1}{1 + x} d x

\int_{- 1}^{1} e^{u + 1} d u

x \to 2 lim (\frac{x ^{2} + 1}{x - 2})

\frac{\partial}{\partial x} (x - \frac{2 y + 6 x}{13})

y = ln (\frac{x}{1 + x ^{2}})

What is the derivative of 2t+4/3 t^{3/2}+(t^2)/2 ?
The derivative of 2t+4/3 t^{3/2}+(t^2)/2 is 2+2t^{1/2}+t
What is the first derivative of 2t+4/3 t^{3/2}+(t^2)/2 ?
The first derivative of 2t+4/3 t^{3/2}+(t^2)/2 is 2+2t^{1/2}+t