What is expand-sin(x-y)(1-(dy)/(dx)) ?

The solution to expand-sin(x-y)(1-(dy)/(dx)) is -sin(x-y)+sin(x-y)(dy)/(dx)

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expand-sin(x-y)(1-(dy)/(dx))

expand

- sin (x - y) (1 - \frac{d y}{d x})

- sin (x - y) + sin (x - y) \frac{d y}{d x}

Solution steps

- sin (x - y) (1 - \frac{d y}{d x})

Apply the distributive law:

a (b - c) = ab - a c

a = - sin (x - y), b = 1, c = \frac{d y}{d x}

= - sin (x - y) \cdot 1 - (- sin (x - y)) \frac{d y}{d x}

Apply minus-plus rules

- (- a) = a

= - 1 \cdot sin (x - y) + sin (x - y) \frac{d y}{d x}

Multiply:

1 \cdot sin (x - y) = sin (x - y)

= - sin (x - y) + sin (x - y) \frac{d y}{d x}

(8 x^{3} - 79 + 0.5 x) d x

(e^{a} (cos (b) + i sin (b)))^{l n (x)}

\frac{1}{s ^{2} ( s + 8 )}

(2 cos (2 x) cos (x) - cos (3 x)) sec (x)

\frac{π ( 9 - x ^{2} ) ( x + 3 )}{3}

What is expand-sin(x-y)(1-(dy)/(dx)) ?
The solution to expand-sin(x-y)(1-(dy)/(dx)) is -sin(x-y)+sin(x-y)(dy)/(dx)