What is the derivative of ln(x+sin(pix)) ?

The derivative of ln(x+sin(pix)) is 1/x+cos(pix)pi

What is the first derivative of ln(x+sin(pix)) ?

The first derivative of ln(x+sin(pix)) is 1/x+cos(pix)pi

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\frac{d}{d x} (ln (x) + sin (π x))

\frac{1}{x} + cos (π x) π

Solution steps

\frac{d}{d x} (ln (x) + sin (π x))

Apply the Sum/Difference Rule:

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

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

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

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

= \frac{1}{x} + cos (π x) π

\int \frac{5 x ^{2} - 11 x + 5}{x ^{3} - 4 x ^{2} + 5 x - 2} d x

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

x \to 2 lim (\frac{1}{x ^{3}})

\int_{- 1}^{3} (- 3 x^{2} + 4 x - 5) d x

\int 6 (x + 2) ln (x + 2) d x

What is the derivative of ln(x+sin(pix)) ?
The derivative of ln(x+sin(pix)) is 1/x+cos(pix)pi
What is the first derivative of ln(x+sin(pix)) ?
The first derivative of ln(x+sin(pix)) is 1/x+cos(pix)pi