Name: Differentiation of Exponential Functions
Uploaded: 2019-07-19
Duration: 12 min 3 s
Description: To know how to find the derivative of exponential functions or multiple functions containing the exponential term. Let's watch this video and explore!

Question

Differentiate the following w.r.t. $x$ :

$\sqrt{4 + \sqrt{4 + \sqrt{4 + x^{2}}}}$

Accepted Answer

Let, $y = \sqrt{4 + \sqrt{4 + \sqrt{4 + x^{2}}}}$

Differentiate the above equation with respect to $x,$

$\Rightarrow \frac{d y}{d x} = \frac{d}{d x} (\sqrt{4 + \sqrt{4 + \sqrt{4 + x^{2}}}})$

$\Rightarrow \frac{d y}{d x} = \frac{1}{2 \sqrt{4 + \sqrt{4 + \sqrt{4 + x^{2}}}}} \frac{d}{d x} (4 + \sqrt{4 + \sqrt{4 + x^{2}}})$

(using Chain rule of differentiation)

$\Rightarrow \frac{d y}{d x} = \frac{1}{2 \sqrt{4 + \sqrt{4 + \sqrt{4 + x^{2}}}}} (\frac{d}{d x} (4) + \frac{d}{d x} (\sqrt{4 + \sqrt{4 + x^{2}}}))$

$\Rightarrow \frac{d y}{d x} = \frac{1}{2 \sqrt{4 + \sqrt{4 + \sqrt{4 + x^{2}}}}} (0 + \frac{1}{2 \sqrt{4 + \sqrt{4 + x^{2}}}} \frac{d}{d x} (4 + \sqrt{4 + x^{2}}))$

$\Rightarrow \frac{d y}{d x} = \frac{1}{2 \sqrt{4 + \sqrt{4 + \sqrt{4 + x^{2}}}}} (\frac{1}{2 \sqrt{4 + \sqrt{4 + x^{2}}}} . \frac{1}{2 \sqrt{4 + x^{2}}} \frac{d}{d x} (4 + x^{2}))$

$\Rightarrow \frac{d y}{d x} = \frac{1}{2 \sqrt{4 + \sqrt{4 + \sqrt{4 + x^{2}}}}} (\frac{1}{2 \sqrt{4 + \sqrt{4 + x^{2}}}} . \frac{1}{2 \sqrt{4 + x^{2}}} (2 x))$

$\Rightarrow \frac{d y}{d x} = \frac{x}{4 \sqrt{4 + \sqrt{4 + \sqrt{4 + x^{2}}}}} (\frac{1}{\sqrt{4 + \sqrt{4 + x^{2}}}}) . (\frac{1}{\sqrt{4 + x^{2}}})$ .

Differentiate the following w.r.t. $x$ :

$\sqrt{4 + \sqrt{4 + \sqrt{4 + x^{2}}}}$

Important Questions on Differentiation

Learn and Prepare for any exam you want !

Differentiate the following w.r.t. x: 4+4+4+x2

Important Questions on Differentiation

Learn and Prepare for any exam you want !

Differentiate the following w.r.t. $x$ :

$\sqrt{4 + \sqrt{4 + \sqrt{4 + x^{2}}}}$