What is the derivative of f(x)=cos(8x^2-16)sin(x^2) ?

The derivative of f(x)=cos(8x^2-16)sin(x^2) is -16xsin(8x^2-16)sin(x^2)+2xcos(x^2)cos(8x^2-16)

What is the first derivative of f(x)=cos(8x^2-16)sin(x^2) ?

The first derivative of f(x)=cos(8x^2-16)sin(x^2) is -16xsin(8x^2-16)sin(x^2)+2xcos(x^2)cos(8x^2-16)

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derivative of

f (x) = cos (8 x^{2} - 16) sin (x^{2})

- 16 x sin (8 x^{2} - 16) sin (x^{2}) + 2 x cos (x^{2}) cos (8 x^{2} - 16)

Solution steps

\frac{d}{d x} (cos (8 x^{2} - 16) sin (x^{2}))

Apply the Product Rule:

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

f = cos (8 x^{2} - 16), g = sin (x^{2})

= \frac{d}{d x} (cos (8 x^{2} - 16)) sin (x^{2}) + \frac{d}{d x} (sin (x^{2})) cos (8 x^{2} - 16)

\frac{d}{d x} (cos (8 x^{2} - 16)) = - sin (8 x^{2} - 16) \cdot 16 x

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

= (- sin (8 x^{2} - 16) \cdot 16 x) sin (x^{2}) + cos (x^{2}) \cdot 2 x cos (8 x^{2} - 16)

Simplify

= - 16 x sin (8 x^{2} - 16) sin (x^{2}) + 2 x cos (x^{2}) cos (8 x^{2} - 16)

What is the derivative of f(x)=cos(8x^2-16)sin(x^2) ?
The derivative of f(x)=cos(8x^2-16)sin(x^2) is -16xsin(8x^2-16)sin(x^2)+2xcos(x^2)cos(8x^2-16)
What is the first derivative of f(x)=cos(8x^2-16)sin(x^2) ?
The first derivative of f(x)=cos(8x^2-16)sin(x^2) is -16xsin(8x^2-16)sin(x^2)+2xcos(x^2)cos(8x^2-16)