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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

\frac{d y}{d x} = x^{2} - y - 2, y (0) = - 1

\int_{0}^{5} 9800 π (5 - y) d y

\int (sin (x) cos^{3} (x)) d x

x \to \infty lim (\frac{( 2 x - 1 ) ( 3 - x )}{( x - 1 ) ( x + 3 )})

y^{^{'}} = \frac{2 x ^{4} e ^{\frac{y}{x}} + x ^{2} y ^{2}}{x ^{3} y}

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