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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (ln (x + y)) = \frac{1 + \frac{d y}{d x}}{x + y}

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

Popular Examples

integral of (2x^3-x^2+2x+4)/(1+x^2)

\int \frac{2 x ^{3} - x ^{2} + 2 x + 4}{1 + x ^{2}} d x

integral of (8x+3)sqrt(4x^2+3x)

\int (8 x + 3) 4 x^{2} + 3 x d x

derivative of (x^2+13x+36/(x^2+8x-9))

\frac{d}{d x} (\frac{x ^{2} + 13 x + 36}{x ^{2} + 8 x - 9})

derivative of 9x^{2/3}derivative of

9 x^{\frac{2}{3}}

tangent of f(x)=6sec(x)tangent of

f (x) = 6 sec (x)

Frequently Asked Questions (FAQ)

What is the derivative of cos(x-y+ln(x+y)) ?
The derivative of cos(x-y+ln(x+y)) is -sin(x-y)(1-(dy)/(dx))+(1+\frac{dy)/(dx)}{x+y}
What is the first derivative of cos(x-y+ln(x+y)) ?
The first derivative of cos(x-y+ln(x+y)) is -sin(x-y)(1-(dy)/(dx))+(1+\frac{dy)/(dx)}{x+y}