Question

consider the following function and express the relationship between a small change in x and the corresponding change in y in the form ( dy = f(x)dx ).
( f(x)=\tan 7x )
( dy=square dx )

Explanation:

Step1: Differentiate the function

Use the chain rule. If \(y = \tan(u)\) and \(u = 7x\), then \(\frac{dy}{du}=\sec^{2}(u)\) and \(\frac{du}{dx}=7\).
By the chain rule \(\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}\).
Substituting \(u = 7x\), we have \(\frac{dy}{dx}=\sec^{2}(7x)\cdot7\).

Answer:

\(7\sec^{2}(7x)\)