What is the derivative of xcos(xcos(y)) ?

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

What is the first derivative of xcos(xcos(y)) ?

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

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

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = cos (x) cos (y)

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

\frac{d x}{d x} = 1

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

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

Simplify

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

\int e^{\frac{x}{2}} d x

\frac{d}{d x} (7 x^{- 12})

\frac{d}{d x} (4 x^{2} + 2 x)

\int lo g_{10} (x) d x

\frac{d}{d x} (arcsec (5 x^{4}))

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