What is the derivative of sin(xcos(3-x^2)) ?

The derivative of sin(xcos(3-x^2)) is cos(x)cos(3-x^2)+2xsin(3-x^2)sin(x)

What is the first derivative of sin(xcos(3-x^2)) ?

The first derivative of sin(xcos(3-x^2)) is cos(x)cos(3-x^2)+2xsin(3-x^2)sin(x)

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

cos (x) cos (3 - x^{2}) + 2 x sin (3 - x^{2}) sin (x)

Solution steps

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

Apply the Product Rule:

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

f = sin (x), g = cos (3 - x^{2})

= \frac{d}{d x} (sin (x)) cos (3 - x^{2}) + \frac{d}{d x} (cos (3 - x^{2})) sin (x)

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

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

= cos (x) cos (3 - x^{2}) + 2 x sin (3 - x^{2}) sin (x)

\frac{d}{d x} (e^{a x} a)

\frac{d y}{d x} = x^{3}

(x + y - 2) d x + (x - y + 4) d y = 0

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

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

What is the derivative of sin(xcos(3-x^2)) ?
The derivative of sin(xcos(3-x^2)) is cos(x)cos(3-x^2)+2xsin(3-x^2)sin(x)
What is the first derivative of sin(xcos(3-x^2)) ?
The first derivative of sin(xcos(3-x^2)) is cos(x)cos(3-x^2)+2xsin(3-x^2)sin(x)