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Popular Calculus >

derivative of xsin(3y)+xe^{y/x}

Solution

derivative of

x \cdot sin (3 y) + x \cdot e^{\frac{y}{x}}

Solution

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

Popular Examples

derivative of y=(x+2)/(x^2)

d er i v a t i v e y = \frac{x + 2}{x ^{2}}

derivative of 1/((s+3)^2)

d er i v a t i v e \frac{1}{( s + 3 ) ^{2}}

derivative of 2x^3-24x^1-35

d er i v a t i v e 2 x^{3} - 24 x^{1} - 35

derivative of 4x^3+5

d er i v a t i v e 4 x^{3} + 5

derivative of (x+1)^3*(5-x)

d er i v a t i v e (x + 1)^{3} \cdot (5 - x)

Frequently Asked Questions (FAQ)

What is the derivative of x*sin(3y)+x*e^{y/x} ?
The derivative of x*sin(3y)+x*e^{y/x} is sin(3y)+e^{y/x}-(ye^{y/x})/x
What is the first derivative of x*sin(3y)+x*e^{y/x} ?
The first derivative of x*sin(3y)+x*e^{y/x} is sin(3y)+e^{y/x}-(ye^{y/x})/x