Differentiate.

{eq}\displaystyle y = 2^{\frac{t}{2}} + t^{\frac{1}{2}} {/eq}

Question:

Rules of Differentiation:

The following are some important rules of differentiation that we need to solve the defined problem of differentiation.

$$\begin{align} & \dfrac{\mathrm{d} }{\mathrm{d} t}(t^n)=nt^{n-1}\ & \left [ \text{Power Rule} \right ]\\[0.3cm] & \dfrac{\mathrm{d} }{\mathrm{d} t}(f(g(t)))=f'(g(t))g'(t)\ & \left [ \text{Chain Rule} \right ]\\[0.3cm] & \dfrac{\mathrm{d} }{\mathrm{d} t}(a^t)=a^t\ln (a) \end{align} $$

Answer and Explanation: 1