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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

= - \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{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)

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

Simplify

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

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

n = 1 \sum \infty n^{n}

\int e^{4 x} sin (6 x) d x

\frac{1}{s ( s ( s + 4 ) + 3 )}

\frac{d}{d x} (11 x^{2} cot (x))

f (x) = 4

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