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

The derivative of x^3cos(x^2) is 3x^2cos(x^2)-2x^4sin(x^2)

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

The first derivative of x^3cos(x^2) is 3x^2cos(x^2)-2x^4sin(x^2)

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derivative of

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

3 x^{2} cos (x^{2}) - 2 x^{4} sin (x^{2})

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

3 x^{2} cos (x^{2}) + (- sin (x^{2}) \cdot 2 x) x^{3} : 3 x^{2} cos (x^{2}) - 2 x^{4} sin (x^{2})

= 3 x^{2} cos (x^{2}) - 2 x^{4} sin (x^{2})

\int \frac{x ^{2}}{25 - 9 x ^{2}} d x

2 y^{^{''}} - 9 y^{^{'}} - 5 y = 0

sec^{2} (π x)

\frac{d}{d x} (\frac{6}{x + 2})

f (x) = (2 + 3 x) (6 - 5 x), at x = 1

What is the derivative of x^3cos(x^2) ?
The derivative of x^3cos(x^2) is 3x^2cos(x^2)-2x^4sin(x^2)
What is the first derivative of x^3cos(x^2) ?
The first derivative of x^3cos(x^2) is 3x^2cos(x^2)-2x^4sin(x^2)