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)

\frac{d y}{d x} = x + \frac{1}{5} y

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

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} + y = 0

f (x) = x^{8} - 46

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

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)