What is the derivative of-1/2 x^4cos(x) ?

The derivative of-1/2 x^4cos(x) is -1/2 (4x^3cos(x)-x^4sin(x))

What is the first derivative of-1/2 x^4cos(x) ?

The first derivative of-1/2 x^4cos(x) is -1/2 (4x^3cos(x)-x^4sin(x))

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

- \frac{1}{2} (4 x^{3} cos (x) - x^{4} sin (x))

Solution steps

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

Simplify

- \frac{1}{2} x^{4} cos (x) : - \frac{x ^{4} cos ( x )}{2}

= \frac{d}{d x} (- \frac{x ^{4} cos ( x )}{2})

Take the constant out:

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

= - \frac{1}{2} \frac{d}{d x} (x^{4} cos (x))

Apply the Product Rule:

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

f = x^{4}, g = cos (x)

= - \frac{1}{2} (\frac{d}{d x} (x^{4}) cos (x) + \frac{d}{d x} (cos (x)) x^{4})

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

= - \frac{1}{2} (4 x^{3} cos (x) + (- sin (x)) x^{4})

Simplify

= - \frac{1}{2} (4 x^{3} cos (x) - x^{4} sin (x))

\int \frac{2}{X} d X

f (x) = 5 e^{5 x}

\int \frac{x ^{3}}{x ^{3} - 1} d x

What is the derivative of-1/2 x^4cos(x) ?
The derivative of-1/2 x^4cos(x) is -1/2 (4x^3cos(x)-x^4sin(x))
What is the first derivative of-1/2 x^4cos(x) ?
The first derivative of-1/2 x^4cos(x) is -1/2 (4x^3cos(x)-x^4sin(x))