What is (\partial)/(\partial a)(cos(a)sin(a+2b)) ?

The answer to (\partial)/(\partial a)(cos(a)sin(a+2b)) is cos(2a+2b)

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(\partial)/(\partial a)(cos(a)sin(a+2b))

\frac{\partial}{\partial a} (cos (a) sin (a + 2 b))

cos (2 a + 2 b)

Solution steps

\frac{\partial}{\partial a} (cos (a) sin (a + 2 b))

Treat

b

as a constant

Apply the Product Rule:

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

f = cos (a), g = sin (a + 2 b)

= \frac{\partial}{\partial a} (cos (a)) sin (a + 2 b) + \frac{\partial}{\partial a} (sin (a + 2 b)) cos (a)

\frac{\partial}{\partial a} (cos (a)) = - sin (a)

\frac{\partial}{\partial a} (sin (a + 2 b)) = cos (a + 2 b)

= (- sin (a)) sin (a + 2 b) + cos (a + 2 b) cos (a)

Simplify

(- sin (a)) sin (a + 2 b) + cos (a + 2 b) cos (a) : cos (2 a + 2 b)

= cos (2 a + 2 b)

\frac{\partial}{\partial x} (3 x^{2} - 2 x y + y^{2} - 8 y)

x \to \infty lim (x + x - x - x)

x \to 2 lim (x^{3} - 1)

F (x) = 3 x^{4} - 65 x^{3}

t + 1

What is (\partial)/(\partial a)(cos(a)sin(a+2b)) ?
The answer to (\partial)/(\partial a)(cos(a)sin(a+2b)) is cos(2a+2b)