What is (\partial)/(\partial x)(9xsin(8x^2y)) ?

The answer to (\partial)/(\partial x)(9xsin(8x^2y)) is 9(sin(8x^2y)+16x^2ycos(8x^2y))

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(\partial)/(\partial x)(9xsin(8x^2y))

\frac{\partial}{\partial x} (9 x sin (8 x^{2} y))

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

Solution steps

\frac{\partial}{\partial x} (9 x sin (8 x^{2} y))

Treat

y

as a constant

Take the constant out:

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

= 9 \frac{\partial}{\partial x} (x sin (8 x^{2} y))

Apply the Product Rule:

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

f = x, g = sin (8 x^{2} y)

= 9 (\frac{\partial}{\partial x} (x) sin (8 x^{2} y) + \frac{\partial}{\partial x} (sin (8 x^{2} y)) x)

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

\frac{\partial}{\partial x} (sin (8 x^{2} y)) = cos (8 x^{2} y) \cdot 16 y x

= 9 (1 \cdot sin (8 x^{2} y) + cos (8 x^{2} y) \cdot 16 y xx)

Simplify

9 (1 \cdot sin (8 x^{2} y) + cos (8 x^{2} y) \cdot 16 y xx) : 9 (sin (8 x^{2} y) + 16 x^{2} y cos (8 x^{2} y))

= 9 (sin (8 x^{2} y) + 16 x^{2} y cos (8 x^{2} y))

e^{3 t} cos (2 t)

\frac{d}{d x} (sin^{2} (e^{s i n^{2} (x)}))

\int 3 x cos^{3} (x^{2} + 2) d x

f (x) = x^{2}, at m (x) = - \frac{1}{2}

\frac{d}{d x} (r^{2} - 8 x^{2})

What is (\partial)/(\partial x)(9xsin(8x^2y)) ?
The answer to (\partial)/(\partial x)(9xsin(8x^2y)) is 9(sin(8x^2y)+16x^2ycos(8x^2y))