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Popular Calculus >

derivative of cos(x+xcos(y)-y)

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Popular Examples

(\partial)/(\partial x)(xyz+9x+8y-4z)

\frac{\partial}{\partial x} (x yz + 9 x + 8 y - 4 z)

laplacetransform f(t)=1

l a pl a ce t r an s f or m f (t) = 1

inverse oflaplace s/((s+1)^5)

in v erse l a pl a ce \frac{s}{( s + 1 ) ^{5}}

integral of sin^3(3x)cos^5(3x)

\int sin^{3} (3 x) cos^{5} (3 x) d x

integral from-2 to 14 of 1/((x+2)^{1/4)}

\int_{- 2}^{14} \frac{1}{( x + 2 ) ^{\frac{1}{4}}} d x

Frequently Asked Questions (FAQ)

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