Question

the derivation of 7x w.r.to x7 is solved using log​

Answer 1

Derivative

Step-by-step explanation:

Suppose $7x=a$ and $x^{7} =b$

We have to find the derivative of $7x$ with respect to $x^{7}$

That means, we have to find $\frac{da}{db}$

So,

                    $\frac{da}{db} =\frac{(\frac{da}{dx} )}{(\frac{db}{dx} )}$

Now,

                    $\frac{da}{dx} =\frac{d(7x)}{dx} \\\frac{da}{dx} =7$

And,

                   $\frac{db}{dx} =\frac{d(x^{7} )}{dx} \\\frac{db}{dx} =7x^{6}$

Therefore,

                  $\frac{da}{db} =\frac{7}{7x^{6} } \\\frac{da}{db} =\frac{1}{x^{6} }$

That means, the derivative of $7x$ with respect to $x^{7}$ will be $\frac{1}{x^{6} }$