What is the derivative of x*sin(y) ?

The derivative of x*sin(y) is sin(y)+xcos(y)(dy)/(dx)

What is the first derivative of x*sin(y) ?

The first derivative of x*sin(y) is sin(y)+xcos(y)(dy)/(dx)

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\frac{d}{d x} (x \cdot sin (y))

sin (y) + x cos (y) \frac{d y}{d x}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = sin (y)

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

\frac{d x}{d x} = 1

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

= 1 \cdot sin (y) + cos (y) \frac{d y}{d x} x

Simplify

= sin (y) + x cos (y) \frac{d y}{d x}

9 x cos (x^{2})

x \to - \infty lim (6^{x})

y^{^{'}} - 3 y = e^{x}

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

f (x) = 4 - x^{2}, at x = 2

What is the derivative of x*sin(y) ?
The derivative of x*sin(y) is sin(y)+xcos(y)(dy)/(dx)
What is the first derivative of x*sin(y) ?
The first derivative of x*sin(y) is sin(y)+xcos(y)(dy)/(dx)