What is the derivative of sin(8xcos(9y)) ?

The derivative of sin(8xcos(9y)) is 8cos(9y)cos(8x)-9sin(9y)sin(8x)(dy)/(dx)

What is the first derivative of sin(8xcos(9y)) ?

The first derivative of sin(8xcos(9y)) is 8cos(9y)cos(8x)-9sin(9y)sin(8x)(dy)/(dx)

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\frac{d}{d x} (sin (8 x) cos (9 y))

8 cos (9 y) cos (8 x) - 9 sin (9 y) sin (8 x) \frac{d y}{d x}

Solution steps

\frac{d}{d x} (sin (8 x) cos (9 y))

Apply the Product Rule:

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

f = sin (8 x), g = cos (9 y)

= \frac{d}{d x} (sin (8 x)) cos (9 y) + \frac{d}{d x} (cos (9 y)) sin (8 x)

\frac{d}{d x} (sin (8 x)) = cos (8 x) \cdot 8

\frac{d}{d x} (cos (9 y)) = - sin (9 y) \cdot 9 \frac{d y}{d x}

= cos (8 x) \cdot 8 cos (9 y) + (- sin (9 y) \cdot 9 \frac{d y}{d x}) sin (8 x)

Simplify

= 8 cos (9 y) cos (8 x) - 9 sin (9 y) sin (8 x) \frac{d y}{d x}

(x^{x} + 1)^{2}

\int x (18 x + 4) d x

\frac{x ^{2}}{2 ( 1 - x )}

x \to - 2 lim (\frac{3}{x - 2})

x \to 0 lim (\frac{( 3 + x ) ^{3} - 8}{x})

What is the derivative of sin(8xcos(9y)) ?
The derivative of sin(8xcos(9y)) is 8cos(9y)cos(8x)-9sin(9y)sin(8x)(dy)/(dx)
What is the first derivative of sin(8xcos(9y)) ?
The first derivative of sin(8xcos(9y)) is 8cos(9y)cos(8x)-9sin(9y)sin(8x)(dy)/(dx)