How do you differentiate $f (x) = e^{({(ln (x^{2} + 3))}^{2})}$ $f(x)=e^(((ln(x^2+3))^2)$ using the chain rule.?

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How do you differentiate $f (x) = e^{({(ln (x^{2} + 3))}^{2})}$ $f(x)=e^(((ln(x^2+3))^2)$ using the chain rule.?

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Answer 1 · 2016-02-27T06:49:54

$e^{{(ln (x^{2} + 3))}^{2}} \cdot 4 x (\frac{ln (x^{2} + 3)}{x^{2} + 3})$ $e^((ln(x^2+3))^2)*4x(ln(x^2+3)/(x^2+3))$

Explanation:

first find the derivative of $({(ln (x^{2} + 3))}^{2})$ $((ln(x^2+3))^2)$ , the expression in the power of e then multiply it with $e^{{(ln (x^{2} + 3))}^{2}}$ $e^((ln(x^2+3))^2)$

Answer 2 · 2016-02-27T07:13:07

Set $u (x) = {(ln (x^{2} + 3))}^{2}$ $u(x)=(ln(x^2+3))^2$ hence

$(\frac{d f}{d x}) = e^{u (x)} \cdot (\frac{d u}{d x})$ $((df)/dx)=e^(u(x))*((du)/dx)$

where

$\frac{d u}{d x} = \frac{4 x ln (x^{2} + 3)}{x^{2} + 3}$ $(du)/dx=[4xln(x^2+3)]/[x^2+3]$

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How do you differentiate $f (x) = e^{({(ln (x^{2} + 3))}^{2})}$ $f(x)=e^(((ln(x^2+3))^2)$ using the chain rule.?

2 Answers

Explanation:

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How do you differentiate f(x)=e^(((ln(x^2+3))^2)f(x)=e((ln(x2+3))2) f(x)=e^(((ln(x^2+3))^2) using the chain rule.?

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How do you differentiate $f (x) = e^{({(ln (x^{2} + 3))}^{2})}$ $f(x)=e^(((ln(x^2+3))^2)$ using the chain rule.?