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Popular >

derivative of 3xsin(y+ln(y^2))

Solution

\frac{d}{d x} (3 x sin (y) + ln (y^{2}))

Solution

3 (sin (y) + x cos (y) \frac{d y}{d x}) + \frac{2 \frac{d y}{d x}}{y}

Solution steps

\frac{d}{d x} (3 x sin (y) + ln (y^{2}))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (3 x sin (y)) + \frac{d}{d x} (ln (y^{2}))

\frac{d}{d x} (3 x sin (y)) = 3 (sin (y) + x cos (y) \frac{d y}{d x})

\frac{d}{d x} (ln (y^{2})) = \frac{2 \frac{d y}{d x}}{y}

= 3 (sin (y) + x cos (y) \frac{d y}{d x}) + \frac{2 \frac{d y}{d x}}{y}

Popular Examples

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x \to 3 - lim (x - 3)

(\partial)/(\partial x)(yln(xz^2))

\frac{\partial}{\partial x} (y ln (x z^{2}))

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\int \frac{1}{( 1 - x ) ^{6}} d x

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x \to 1 lim (3 (0.85)^{2} + 3)

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Frequently Asked Questions (FAQ)

What is the derivative of 3xsin(y+ln(y^2)) ?
The derivative of 3xsin(y+ln(y^2)) is 3(sin(y)+xcos(y)(dy}{dx})+(2\frac{dy)/(dx))/y
What is the first derivative of 3xsin(y+ln(y^2)) ?
The first derivative of 3xsin(y+ln(y^2)) is 3(sin(y)+xcos(y)(dy}{dx})+(2\frac{dy)/(dx))/y