What is (\partial)/(\partial x)(9xcos(3xy)) ?

The answer to (\partial)/(\partial x)(9xcos(3xy)) is 9(cos(3xy)-3xysin(3xy))

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(\partial)/(\partial x)(9xcos(3xy))

\frac{\partial}{\partial x} (9 x cos (3 x y))

9 (cos (3 x y) - 3 x y sin (3 x y))

Solution steps

\frac{\partial}{\partial x} (9 x cos (3 x y))

Treat

y

as a constant

Take the constant out:

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

= 9 \frac{\partial}{\partial x} (x cos (3 x y))

Apply the Product Rule:

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

f = x, g = cos (3 x y)

= 9 (\frac{\partial}{\partial x} (x) cos (3 x y) + \frac{\partial}{\partial x} (cos (3 x y)) x)

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (cos (3 x y)) = - sin (3 x y) \cdot 3 y

= 9 (1 \cdot cos (3 x y) + (- sin (3 x y) \cdot 3 y) x)

Simplify

= 9 (cos (3 x y) - 3 x y sin (3 x y))

\frac{d}{d x} ((x + a)^{2})

4 t

sin^{2} (5 t)

\int \frac{sin ( x ) + cos ^{2} ( x )}{cos ^{2} ( x )} d x

f (x) = \frac{6}{x}, (1, 6)

What is (\partial)/(\partial x)(9xcos(3xy)) ?
The answer to (\partial)/(\partial x)(9xcos(3xy)) is 9(cos(3xy)-3xysin(3xy))