Question

Compute the derivative of $6x^{100}-x^{55}+x$.

Answer 1

Let $f\left(x\right)=6x^{100}-x^{55}+x$
Power rule : Differentiation of $x^n$ with respect to $x$ is $n{x}^{n-1}$
Differentiation of $f\left(x\right)$ with respect to $x$
$\Rightarrow f^{\prime }\left(x\right)=6\left(100\right)x^{100-1}-55x^{55-1}+1\cdot x^{1-1}$
$\Rightarrow f^{\prime }\left(x\right)=600x^{99}-55x^{54}+x^0$
$\Rightarrow f^{\prime }\left(x\right)=600x^{99}-55x^{54}+1$