Name: Product and Quotient Rule of Differentiation
Uploaded: 2019-07-19
Duration: 6 min 35 s
Description: Did you know that temperature variation can be checked using derivatives? Wow! That’s amazing! Watch the video to learn more about the product and quotient r...

Question

Differentiate $\tan (2 x + 1)$ using first principle.

Accepted Answer

We have to differentiate $\tan (2 x + 1)$ using first principle of differentiation

$f (x) = \tan (2 x + 1)$

$\frac{d}{d x} (f (x)) = \lim_{h \to 0} \frac{f (x + h) - f (x)}{h}$

$= \lim_{h \to 0} \frac{\tan (2 x + 2 h + 1) - \tan (2 x + 1)}{h}$

$= \lim_{h \to 0} \frac{\frac{\sin (2 x + 2 h + 1)}{\cos (2 x + 2 h + 1)} - \frac{\sin (2 x + 1)}{\cos (2 x + 1)}}{h}$

$= \lim_{h \to 0} \frac{\sin (2 x + 2 h + 1) \cos (2 x + 1) - \cos (2 x + 2 h + 1) \sin (2 x + 1)}{h \cos (2 x + 2 h + 1) \cos (2 x + 1)}$

$= \lim_{h \to 0} \frac{\sin (2 x + 2 h + 1 - 2 x - 1)}{h \cos (2 x + 2 h + 1) \cos (2 x + 1)}$

$= \frac{1}{\cos (2 x + 1)} \lim_{h \to 0} \frac{\sin (2 h)}{2 h} \times 2 \lim_{h \to 0} \frac{1}{\cos (2 x + 2 h + 1)}$

$= \frac{1}{\cos (2 x + 1)} \times 2 \times \frac{1}{\cos (2 x + 1)}$

$= \frac{2}{\cos^{2} (2 x + 1)}$

$= 2 \sec^{2} (2 x + 1)$

Differentiate $\tan (2 x + 1)$ using first principle.

Important Questions on Derivatives

Learn and Prepare for any exam you want !

Differentiate tan(2x+1) using first principle.

Important Questions on Derivatives

Learn and Prepare for any exam you want !

Differentiate $\tan (2 x + 1)$ using first principle.