Question

If f'(0) = 5 and F(x) = f(3x), what is F'(0)?

Answer 1

Answer:

F'(0)=15

Step-by-step explanation:

Differentiate $F(x)$ with respect to $x$.

$F'(x)=3f'(x)$

Subsitute $0$ for $x$ in the above equation.

$F'(0)=3f'(0)\\=3\cdot5\\=15$

Answer 2

Answer:

$\displaystyle F'(0) = 15$

Step-by-step explanation:

We are given that:

$f'(0) = 5 \text{ and } F(x) = f(3x)$

And we want to find F'(0).

First, find F(x):

$\displaystyle F'(x) = \frac{d}{dx}\left[ f(3x)]$

From the chain rule:

$\displaystyle \begin{aligned} F'(x) &= f'(3x) \cdot \frac{d}{dx} \left[ 3x\right] \\ \\ &= 3f'(3x)\end{aligned}$

Then:

$\displaystyle \begin{aligned} F'(0) & = 3f'(3(0)) \\ \\ & = 3f'(0) \\ \\ & = 3(5) \\ \\ & = 15\end{aligned}$

In conclusion, F'(0) = 15.