Question

Differentiate this equation w.r.t to x

x³.logx
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Answer 1

Differentiate this equation w.r.t to x

x³.logx

$y = x {}^{3} .logx \\ differentating \: wrt \: x \\ dy \div dx = d(x {}^{3} .logx \div dx) \\ using \: product \: rule \\ dy \div dx = x {}^{3} 1 \div x + logx3x {}^{2}$

dy/dx=x^3/x+logx3x^2

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Answer 2

${\sf{\underline{Differential \:Equations}}}$

To find : derivative of x³. Log x

Let y = x³ . Log x

We will use the product rule here.

${\bold{Product \:Rule}}$→

$\frac{d}{dx} (uv) = u (\frac{dv}{dx} ) + v( \frac{du}{dx} )$

Applying the same rule to the given equation we have ,

$= > \frac{dy}{dx} = x {}^{3} \frac{d}{dx} (log \: x) + log \: x \: \frac{d}{dx} (x {}^{3} ) \\ \\ = > \frac{dy}{dx} = x {}^{3} \times \frac{1}{x} + log \: x \times 3x {}^{2} \\ = > \frac{dy}{dx} = x {}^{2} + 3x {}^{2} .logx$

Taking x² common we get ,

=> x² ( 1 + 3 log x)

•°• ${\underline{\bold{The\:Derivative\:of\:the\:given \:equation \:is}}}$ →

x² ( 1 + 3 Logx)

Points to Remember :

• Derivative of log x = 1/x
• dy/dx (xⁿ) = nx^(n-1)

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