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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\int (e^{- x} + 4^{x}) d x

G (r) = r + 4 r

\int \frac{1}{x ^{2} - 8 x} d x

\frac{\partial}{\partial x} (2 y cos (x y))

x \to - 3 lim (- 4 x + 8)

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