What is the derivative of x^2sin(y) ?

The derivative of x^2sin(y) is 2xsin(y)+cos(y)(dy)/(dx)x^2

What is the first derivative of x^2sin(y) ?

The first derivative of x^2sin(y) is 2xsin(y)+cos(y)(dy)/(dx)x^2

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

2 x sin (y) + cos (y) \frac{d y}{d x} x^{2}

Solution steps

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

Apply the Product Rule:

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

f = x^{2}, g = sin (y)

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

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

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

= 2 x sin (y) + cos (y) \frac{d y}{d x} x^{2}

y^{^{'}} = 100 - y

\frac{d}{d x} ((2 x + 1)^{5} (x^{4} - 3)^{6})

\int (\frac{60}{2 x + 5} - 4) d x

\int 3 x^{3} \cdot 4 x^{4} d x

\frac{\partial}{\partial x} (cos (i y) e^{i x} i)

What is the derivative of x^2sin(y) ?
The derivative of x^2sin(y) is 2xsin(y)+cos(y)(dy)/(dx)x^2
What is the first derivative of x^2sin(y) ?
The first derivative of x^2sin(y) is 2xsin(y)+cos(y)(dy)/(dx)x^2