What is the derivative of y=19sin(x)cos(x) ?

The derivative of y=19sin(x)cos(x) is 19cos(2x)

What is the first derivative of y=19sin(x)cos(x) ?

The first derivative of y=19sin(x)cos(x) is 19cos(2x)

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derivative of

y = 19 sin (x) cos (x)

19 cos (2 x)

Solution steps

\frac{d}{d x} (19 sin (x) cos (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 19 \frac{d}{d x} (sin (x) cos (x))

Apply the Product Rule:

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

f = sin (x), g = cos (x)

= 19 (\frac{d}{d x} (sin (x)) cos (x) + \frac{d}{d x} (cos (x)) sin (x))

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

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

= 19 (cos (x) cos (x) + (- sin (x)) sin (x))

Simplify

19 (cos (x) cos (x) + (- sin (x)) sin (x)) : 19 cos (2 x)

= 19 cos (2 x)

tan (ln (a x + b))

y = 6 - 3 x^{2}, y = 3 x^{2}, x = - 2, x = 2

f (x) = - x^{3} + 8, - 8, 1

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

\int \frac{ln ( y ^{3} )}{8 y} d y

What is the derivative of y=19sin(x)cos(x) ?
The derivative of y=19sin(x)cos(x) is 19cos(2x)
What is the first derivative of y=19sin(x)cos(x) ?
The first derivative of y=19sin(x)cos(x) is 19cos(2x)