What is the derivative of sin(y-ysin(x)) ?

The derivative of sin(y-ysin(x)) is cos(y)(dy)/(dx)-sin(x)(dy)/(dx)-cos(x)y

What is the first derivative of sin(y-ysin(x)) ?

The first derivative of sin(y-ysin(x)) is cos(y)(dy)/(dx)-sin(x)(dy)/(dx)-cos(x)y

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Popular >

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

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

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

\int sec^{5} (2 x) tan (2 x) d x

x \to 1 + lim (\frac{6}{x - 1})

\int \frac{1}{9} e^{3 x} d x

\frac{d}{d x} (26 x - x^{2})

f (x) = (\frac{e ^{4 x}}{x ^{6}})^{3}

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