What is the derivative of 2/5 x^3cos(x) ?

The derivative of 2/5 x^3cos(x) is 2/5 (3x^2cos(x)-x^3sin(x))

What is the first derivative of 2/5 x^3cos(x) ?

The first derivative of 2/5 x^3cos(x) is 2/5 (3x^2cos(x)-x^3sin(x))

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\frac{d}{d x} (\frac{2}{5} x^{3} cos (x))

\frac{2}{5} (3 x^{2} cos (x) - x^{3} sin (x))

Solution steps

\frac{d}{d x} (\frac{2}{5} x^{3} cos (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{2}{5} \frac{d}{d x} (x^{3} cos (x))

Apply the Product Rule:

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

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

= \frac{2}{5} (\frac{d}{d x} (x^{3}) cos (x) + \frac{d}{d x} (cos (x)) x^{3})

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

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

= \frac{2}{5} (3 x^{2} cos (x) + (- sin (x)) x^{3})

Simplify

= \frac{2}{5} (3 x^{2} cos (x) - x^{3} sin (x))

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

\frac{d}{d x} (\frac{6 x ^{2} + 8 x + 8}{x})

\frac{d}{d x} (84 x^{6} + 12 x^{3} - 24 x^{2})

\int (1 - 2 x)^{4} d x

\int \frac{1}{( 4 + 9 x ^{2} )} d x

What is the derivative of 2/5 x^3cos(x) ?
The derivative of 2/5 x^3cos(x) is 2/5 (3x^2cos(x)-x^3sin(x))
What is the first derivative of 2/5 x^3cos(x) ?
The first derivative of 2/5 x^3cos(x) is 2/5 (3x^2cos(x)-x^3sin(x))