What is the derivative of f(x)=(-x^3+x^2+x)cos(x) ?

The derivative of f(x)=(-x^3+x^2+x)cos(x) is cos(x)(-3x^2+2x+1)-sin(x)(-x^3+x^2+x)

What is the first derivative of f(x)=(-x^3+x^2+x)cos(x) ?

The first derivative of f(x)=(-x^3+x^2+x)cos(x) is cos(x)(-3x^2+2x+1)-sin(x)(-x^3+x^2+x)

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derivative of

f (x) = (- x^{3} + x^{2} + x) cos (x)

cos (x) (- 3 x^{2} + 2 x + 1) - sin (x) (- x^{3} + x^{2} + x)

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (- x^{3} + x^{2} + x) = - 3 x^{2} + 2 x + 1

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

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

Simplify

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

\int x^{2} - 2 x + 1 d x

\int \frac{1}{x + 6} d x

\frac{\partial}{\partial x} (x^{- 2})

\int x^{- 0.9} d x

t a y l or (1 - x) e^{x + \frac{x ^{2}}{2} + \frac{x ^{3}}{3}}

What is the derivative of f(x)=(-x^3+x^2+x)cos(x) ?
The derivative of f(x)=(-x^3+x^2+x)cos(x) is cos(x)(-3x^2+2x+1)-sin(x)(-x^3+x^2+x)
What is the first derivative of f(x)=(-x^3+x^2+x)cos(x) ?
The first derivative of f(x)=(-x^3+x^2+x)cos(x) is cos(x)(-3x^2+2x+1)-sin(x)(-x^3+x^2+x)