Question

find the derivative of
$f(x)=(x + 5)^{60}$
$f(x)=$

Explanation:

Step1: Apply chain - rule

Let $u = x + 5$, then $y = u^{60}$. The chain - rule states that $\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}$.

Step2: Find $\frac{dy}{du}$

Differentiate $y = u^{60}$ with respect to $u$. Using the power rule $\frac{d}{du}(u^n)=nu^{n - 1}$, we get $\frac{dy}{du}=60u^{59}$.

Step3: Find $\frac{du}{dx}$

Differentiate $u = x + 5$ with respect to $x$. $\frac{du}{dx}=1$.

Step4: Calculate $\frac{dy}{dx}$

Substitute $\frac{dy}{du}$ and $\frac{du}{dx}$ into the chain - rule formula: $\frac{dy}{dx}=60u^{59}\cdot1$. Since $u = x + 5$, we have $f^{\prime}(x)=60(x + 5)^{59}$.

Answer:

$60(x + 5)^{59}$