Q. Given that $\frac{d}{dx}f(x) = f^{'}(x)$. The relationship $f^{'}(a + b) = f^{'}(a) + f^{'}(b)$ is valid, if $f(x)$ is equal to
A) $x$
B) $x^{2}$
C) $x^{3}$
D) $x^{4}$
Explanation
(b)
Let $f(x) = x^{2}$
On differentiating w.r.t. $x$, we get
$f^{'}(x) = 2x$
Given that, $f^{'}(a + b) = f^{'}(a) + f^{'}(b)$
$\Rightarrow 2(a + b) = 2a + 2b$
$\Rightarrow 2a + 2b = 2a + 2b$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.