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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

f = cos (x - x^{2}), g = 1 - 2 x

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

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

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

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

Simplify

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

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

x \to 0 lim (x^{13 x})

x \to 0 lim (\frac{1}{x} ln (1 - 2 x))

y^{^{'}} = y^{(\frac{5}{3})}

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

\frac{\partial}{\partial x} (cos (x + y^{3}))

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