Solve- d-x - -x - -x - -x dx

dydx = 12√(x+√(x+√(x+√(x)))) + (1+12√(x+√(x+√(x))))(12√(x+√(x)))(12√(x)) #160; dydx = (1+2√(x+√(x+√(x))))(1+2√(x+√(x)))(1+2√(x))8(√(x+√(x+√(x+√(x))) ...

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Byju's Answer

Standard XII

Mathematics

Chain Rule of Differentiation

Solve: d√x ...

Question

Solve: $\frac{d (\sqrt{x + \sqrt{x + \sqrt{x + \sqrt{x}}}})}{d x}$

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Solution

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

$\frac{d y}{d x} = \frac{(1 + 2 \sqrt{x + \sqrt{x + \sqrt{x}}}) (1 + 2 \sqrt{x + \sqrt{x}}) (1 + 2 \sqrt{x})}{8 (\sqrt{x + \sqrt{x + \sqrt{x + \sqrt{x}}}}) (\sqrt{x + \sqrt{x + \sqrt{x}}}) (\sqrt{x + \sqrt{x}}) \sqrt{x}}$

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Solve: d(√x+√x+√x+√x)dx

dydx=12√x+√x+√x+√x+(1+12√x+√x+√x)(12√x+√x)(12√x)dydx=(1+2√x+√x+√x)(1+2√x+√x)(1+2√x)8(√x+√x+√x+√x)(√x+√x+√x)(√x+√x)√x

Solve: $\frac{d (\sqrt{x + \sqrt{x + \sqrt{x + \sqrt{x}}}})}{d x}$