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

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

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

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

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derivative of

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

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

Solution steps

\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) - x^{4} sin (x)

\int e^{- 2 x} d x

\frac{d y}{d t} + y = t

\int 18 cos (x) d x

\frac{df}{d x} = 4 x^{2} - 5 x + lo g_{10} (x)

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

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