Question

calculate the derivative of the following function. y = √(7x + 15) dy/dx = □

Explanation:

Step1: Rewrite the function

Rewrite $y = \sqrt{7x + 15}$ as $y=(7x + 15)^{\frac{1}{2}}$.

Step2: Apply the chain - rule

The chain - rule states that if $y = u^{\frac{1}{2}}$ and $u = 7x+15$, then $\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}$. First, find $\frac{dy}{du}$: $\frac{dy}{du}=\frac{1}{2}u^{-\frac{1}{2}}$. Second, find $\frac{du}{dx}$: $\frac{du}{dx}=7$.

Step3: Calculate $\frac{dy}{dx}$

Substitute $u = 7x + 15$ back into $\frac{dy}{du}$ and multiply by $\frac{du}{dx}$. So $\frac{dy}{dx}=\frac{1}{2}(7x + 15)^{-\frac{1}{2}}\cdot7=\frac{7}{2\sqrt{7x + 15}}$.

Answer:

$\frac{7}{2\sqrt{7x + 15}}$