What is the derivative of (8x-2x^2cos(y)) ?

The derivative of (8x-2x^2cos(y)) is cos(y)(8-4x)-sin(y)(dy)/(dx)(8x-2x^2)

What is the first derivative of (8x-2x^2cos(y)) ?

The first derivative of (8x-2x^2cos(y)) is cos(y)(8-4x)-sin(y)(dy)/(dx)(8x-2x^2)

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\frac{d}{d x} ((8 x - 2 x^{2}) cos (y))

cos (y) (8 - 4 x) - sin (y) \frac{d y}{d x} (8 x - 2 x^{2})

Solution steps

\frac{d}{d x} ((8 x - 2 x^{2}) cos (y))

Apply the Product Rule:

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

f = 8 x - 2 x^{2}, g = cos (y)

= \frac{d}{d x} (8 x - 2 x^{2}) cos (y) + \frac{d}{d x} (cos (y)) (8 x - 2 x^{2})

\frac{d}{d x} (8 x - 2 x^{2}) = 8 - 4 x

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

= (8 - 4 x) cos (y) + (- sin (y) \frac{d y}{d x}) (8 x - 2 x^{2})

Simplify

= cos (y) (8 - 4 x) - sin (y) \frac{d y}{d x} (8 x - 2 x^{2})

y = (x^{3} + 8) e^{x}

\int (x^{3} + 4)^{4} (3 x^{2}) d x

\frac{d}{d x} (x x)

\int 3 d x

x \to 0 - lim (e^{\frac{8}{x}})

What is the derivative of (8x-2x^2cos(y)) ?
The derivative of (8x-2x^2cos(y)) is cos(y)(8-4x)-sin(y)(dy)/(dx)(8x-2x^2)
What is the first derivative of (8x-2x^2cos(y)) ?
The first derivative of (8x-2x^2cos(y)) is cos(y)(8-4x)-sin(y)(dy)/(dx)(8x-2x^2)