Question

If y = tanx then dy/dx at x = π/4 is
a) 6
b) 2
c) 1
d) -3​

Answer 1

Solution:

We are given that:

$\rm\longrightarrow f(x) = \tan(x)$

Differentiating both sides with respect to x, we get:

$\rm\longrightarrow f'(x)= \sec^{2}(x)$

Now, plugging x = π/4, we get:

$\rm\longrightarrow f'\bigg(\dfrac{\pi}{4}\bigg)= \sec^{2}\bigg(\dfrac{\pi}{4}\bigg)$

$\rm\longrightarrow f'\bigg(\dfrac{\pi}{4}\bigg)=(\sqrt{2})^{2}$

$\rm\longrightarrow f'\bigg(\dfrac{\pi}{4}\bigg)=2$

Which is our required answer.

Learn More:

$\begin{gathered}\boxed{\begin{array}{c|c}\bf f(x)&\bf\dfrac{d}{dx}f(x)\\ \\ \frac{\qquad\qquad}{}&\frac{\qquad\qquad}{}\\ \sf k&\sf0\\ \\ \sf sin(x)&\sf cos(x)\\ \\ \sf cos(x)&\sf-sin(x)\\ \\ \sf tan(x)&\sf{sec}^{2}(x)\\ \\ \sf cot(x)&\sf-{cosec}^{2}(x)\\ \\ \sf sec(x)&\sf sec(x)tan(x)\\ \\ \sf cosec(x)&\sf-cosec(x)cot(x)\\ \\ \sf\sqrt{x}&\sf\dfrac{1}{2\sqrt{x}}\\ \\ \sf log(x)&\sf\dfrac{1}{x}\\ \\ \sf{e}^{x}&\sf{e}^{x}\end{array}}\\ \end{gathered}$