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

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Popular >

derivative of

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

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}

(\frac{x + 1}{x ^{2} + 3}) - 3

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

(x^{6} + 3 x^{2} - x + 3)^{^{'}}

\frac{t ^{2} + 1}{t ^{2}}

\frac{d}{d a} (3 cos^{2} (a) - sin^{2} (a))

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