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Popular >

derivative of x^3-2xsqrt(y+3)

Solution

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

Solution

3 x^{2} - 2 y + 3 - \frac{x \frac{d y}{d x}}{y + 3}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

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

Simplify

= 3 x^{2} - 2 y + 3 - \frac{x \frac{d y}{d x}}{y + 3}

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\int (3 x + 4)^{\frac{5}{2}} d x

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\int_{0}^{2} (2 x - x^{2}) d x

limit as x approaches 1+of (x-1)/(x+1)

x \to 1 + lim (\frac{x - 1}{x + 1})

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\frac{3 s - 1}{s ^{2} - 8 s + 21}

Frequently Asked Questions (FAQ)

What is the derivative of x^3-2xsqrt(y+3) ?
The derivative of x^3-2xsqrt(y+3) is 3x^2-2sqrt(y+3)-(x\frac{dy)/(dx)}{sqrt(y+3)}
What is the first derivative of x^3-2xsqrt(y+3) ?
The first derivative of x^3-2xsqrt(y+3) is 3x^2-2sqrt(y+3)-(x\frac{dy)/(dx)}{sqrt(y+3)}