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Popular Calculus >

derivative of xcos(pix+1)

Solution

\frac{d}{d x} (x cos (π x) + 1)

Solution

- π x sin (π x) + cos (π x)

Solution steps

\frac{d}{d x} (x cos (π x) + 1)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x cos (π x)) + \frac{d}{d x} (1)

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

\frac{d}{d x} (1) = 0

= cos (π x) - π x sin (π x) + 0

Simplify

= - π x sin (π x) + cos (π x)

Graph

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x \to 4 + lim (\frac{2}{x ^{2} - 16})

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x \to \infty lim (x^{3 x})

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Frequently Asked Questions (FAQ)

What is the derivative of xcos(pix+1) ?
The derivative of xcos(pix+1) is -pixsin(pix)+cos(pix)
What is the first derivative of xcos(pix+1) ?
The first derivative of xcos(pix+1) is -pixsin(pix)+cos(pix)