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Popular >

derivative of ln(x+y^2)

Solution

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

Solution

\frac{1 + 2 y \frac{d y}{d x}}{x + y ^{2}}

Solution steps

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

Apply the chain rule:

\frac{1}{x + y ^{2}} \frac{d}{d x} (x + y^{2})

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

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

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

Simplify

\frac{1}{x + y ^{2}} (1 + 2 y \frac{d y}{d x}) : \frac{1 + 2 y \frac{d y}{d x}}{x + y ^{2}}

= \frac{1 + 2 y \frac{d y}{d x}}{x + y ^{2}}

Popular Examples

derivative of ln|sec(x+tan(x)|)

\frac{d}{d x} (ln ∣ sec (x) + tan (x) ∣)

x(dy)/(dx)=y^2-y,y(1/4)= 1/4

x \frac{d y}{d x} = y^{2} - y, y (\frac{1}{4}) = \frac{1}{4}

derivative of x^2+ax+b derivative of

x^{2} + a x + b

(\partial)/(\partial x)((e^x)/(y+x^7))

\frac{\partial}{\partial x} (\frac{e ^{x}}{y + x ^{7}})

tangent of 4x^3-18x^2-48x tangent of

4 x^{3} - 18 x^{2} - 48 x

Frequently Asked Questions (FAQ)

What is the derivative of ln(x+y^2) ?
The derivative of ln(x+y^2) is (1+2y\frac{dy)/(dx)}{x+y^2}
What is the first derivative of ln(x+y^2) ?
The first derivative of ln(x+y^2) is (1+2y\frac{dy)/(dx)}{x+y^2}