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Popular >

d/(da)(sin(a)cos(a))

Solution

\frac{d}{d a} (sin (a) cos (a))

Solution

cos (2 a)

Solution steps

\frac{d}{d a} (sin (a) cos (a))

Apply the Product Rule:

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

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

= \frac{d}{d a} (sin (a)) cos (a) + \frac{d}{d a} (cos (a)) sin (a)

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

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

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

Simplify

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

= cos (2 a)

Popular Examples

(x^2+2xy)dx+xdy=0

(x^{2} + 2 x y) d x + x d y = 0

(\partial)/(\partial x)(x^4+2xy^9)

\frac{\partial}{\partial x} (x^{4} + 2 x y^{9})

derivative of (xy^2)

\frac{d}{d x} ((x y)^{2})

derivative of (-xsin(x)-cos(x))/(4x^2)derivative of

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

integral of x^2-6x+5

\int x^{2} - 6 x + 5 d x

Frequently Asked Questions (FAQ)

What is the d/(da)(sin(a)cos(a)) ?
The d/(da)(sin(a)cos(a)) is cos(2a)
What is the first d/(da)(sin(a)cos(a)) ?
The first d/(da)(sin(a)cos(a)) is cos(2a)