Question

Find the derivate of 7x w.r.t. x7 .

Answer 1

Derivative of $7x$ with respect to $x^{7}$ is $\dfrac{1}{x^{6}}$.

Step-by-step explanation:.

Let, $f(x)=7x$ and $g(x)=x^{7}$.

Now, differentiating both $f(x)$ and $g(x)$ with respect to $x$ we get

$\quad \dfrac{d}{dx}\{f(x)\}=\dfrac{d}{dx}(7x)$

$\Rightarrow f'(x)=7\dfrac{d}{dx}(x^{1})$

$\Rightarrow f'(x)=7\times x^{1-1}$

$\Rightarrow f'(x)=7\times x^{0}$

$\Rightarrow f'(x)=7\times 1$

$\Rightarrow \boxed{f'(x)=7}$

and $\dfrac{d}{dx}\{g(x)\}=\dfrac{d}{dx}(x^{7})$

$\Rightarrow g'(x)=7\times x^{7-1}$

$\Rightarrow g'(x)=7\times x^{6}$

$\Rightarrow \boxed{g'(x)=7x^{6}}$

So, the derivative of $f(x)=7x$ with respect to $g(x)=x^{7}$ is

$\quad \dfrac{f'(x)}{g'(x)}=\dfrac{7}{7x^{6}}$

$\Rightarrow \boxed{\dfrac{f'(x)}{g'(x)}=\frac{1}{x^{6}}}$

Answer 2

Answer:

Step-by-step explanation: