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Popular >

derivative of sin(x-xsin(y))

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

Popular Examples

limit as x approaches 4 of (2x+1)/(3x+3)

x \to 4 lim (\frac{2 x + 1}{3 x + 3})

(dy}{dx}=\frac{e^x)/y

\frac{d y}{d x} = \frac{e ^{x}}{y}

integral from-infinity to 18 of xe^{x/9}

\int_{- \infty}^{18} x e^{\frac{x}{9}} d x

derivative of (x^2-10x+9sqrt(25-x^2))

\frac{d}{d x} ((x^{2} - 10 x + 9) 25 - x^{2})

integral of (xcos^2(y)-sin(y))

\int (x cos^{2} (y) - sin (y)) d x

Frequently Asked Questions (FAQ)

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