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Popular >

derivative of x^3+xe^y-2y

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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

Popular Examples

integral of 1/((x^2+4)^2)

\int \frac{1}{( x ^{2} + 4 ) ^{2}} d x

integral of 6x(-x^2+5)^7

\int 6 x (- x^{2} + 5)^{7} d x

x^2-3xy+x(dy)/(dx)=0

x^{2} - 3 x y + x \frac{d y}{d x} = 0

limit as x approaches 2 of (2-x)/(x-2)

x \to 2 lim (\frac{2 - x}{x - 2})

f (x) = - 4 cos (2 x)

Frequently Asked Questions (FAQ)

What is the derivative of x^3+xe^y-2y ?
The derivative of x^3+xe^y-2y is 3x^2+e^y+e^yx(dy)/(dx)-2(dy)/(dx)
What is the first derivative of x^3+xe^y-2y ?
The first derivative of x^3+xe^y-2y is 3x^2+e^y+e^yx(dy)/(dx)-2(dy)/(dx)