If y = x x 2 , then d x d y is equal to

Consider y = x x 2 ⇒ ln y = x 2 ln x y 1 d x d y = 2 x ln x + x 2 ⋅ x 1 = x ( 1 + 2 ln x ) d x d y = x x 2 ⋅ x ( 1 + 2 ln x ) = x x 2 + 1 ( 1 + 2 ln x )

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MathematicsDifferentiationParametric/Determinant/Logarithmic InverseMedium2 minPYQ_2011

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If $y = x^{x^{2}}$ , then $\frac{d y}{d x}$ is equal to

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Consider $y = x^{x^{2}} \Rightarrow ln y = x^{2} ln x$ $\frac{1}{y} \frac{d y}{d x} = 2 x ln x + x^{2} \cdot \frac{1}{x} = x (1 + 2 ln x) \frac{d y}{d x} = x^{x^{2}} \cdot x (1 + 2 ln x) = x^{x^{2} + 1} (1 + 2 ln x)$

Stream:BITSATSubject:MathematicsTopic:DifferentiationSubtopic:Parametric/Determinant/Logarithmic Inverse

⏱ 2mℹ️ Source: PYQ_2011

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