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Popular >

derivative of cos(x+ln(cos(x))+xsin(x))

Solution

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

Solution

x cos (x) - tan (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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

Simplify

= x cos (x) - tan (x)

Popular Examples

integral of (x^3)/(1+x^3)

\int \frac{x ^{3}}{1 + x ^{3}} d x

limit as x approaches 1 of x^2+2x-2

x \to 1 lim (x^{2} + 2 x - 2)

tangent of f(x)=4e^x-x^{16}x,\at x=0 tangent of

f (x) = 4 e^{x} - x^{16} x, at x = 0

(\partial)/(\partial x)(pi*(x/2)^2h)

\frac{\partial}{\partial x} (π \cdot (\frac{x}{2})^{2} h)

derivative of 1/(4x^2+3x)derivative of

\frac{1}{4 x ^{2} + 3 x}

Frequently Asked Questions (FAQ)

What is the derivative of cos(x+ln(cos(x))+xsin(x)) ?
The derivative of cos(x+ln(cos(x))+xsin(x)) is xcos(x)-tan(x)
What is the first derivative of cos(x+ln(cos(x))+xsin(x)) ?
The first derivative of cos(x+ln(cos(x))+xsin(x)) is xcos(x)-tan(x)