What is the derivative of y=xln(x)cos(x) ?

The derivative of y=xln(x)cos(x) is ln(x)cos(x)+cos(x)-xsin(x)ln(x)

What is the first derivative of y=xln(x)cos(x) ?

The first derivative of y=xln(x)cos(x) is ln(x)cos(x)+cos(x)-xsin(x)ln(x)

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derivative of

y = x ln (x) cos (x)

ln (x) cos (x) + cos (x) - x sin (x) ln (x)

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

1 \cdot ln (x) cos (x) + (\frac{cos ( x )}{x} - sin (x) ln (x)) x : ln (x) cos (x) + cos (x) - x sin (x) ln (x)

= ln (x) cos (x) + cos (x) - x sin (x) ln (x)

\int \frac{3 x ^{3} + 5 x}{x ^{2} - x - 2} d x

x \to - \infty lim (arccos (x))

\int \frac{x ^{2} - 15 L}{x + 7} d x

\int \frac{x ^{2}}{( 1 - 25 x ^{2} ) ^{\frac{3}{2}}} d x

\frac{1 - 3 x - x ^{2}}{x ^{2} - 3}

What is the derivative of y=xln(x)cos(x) ?
The derivative of y=xln(x)cos(x) is ln(x)cos(x)+cos(x)-xsin(x)ln(x)
What is the first derivative of y=xln(x)cos(x) ?
The first derivative of y=xln(x)cos(x) is ln(x)cos(x)+cos(x)-xsin(x)ln(x)