What is the derivative of (x-1tan(x)+xsin(pix)) ?

The derivative of (x-1tan(x)+xsin(pix)) is tan(x)+sec^2(x)(x-1)+sin(pix)+pixcos(pix)

What is the first derivative of (x-1tan(x)+xsin(pix)) ?

The first derivative of (x-1tan(x)+xsin(pix)) is tan(x)+sec^2(x)(x-1)+sin(pix)+pixcos(pix)

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

tan (x) + sec^{2} (x) (x - 1) + sin (π x) + π x cos (π x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} ((x - 1) tan (x)) = tan (x) + sec^{2} (x) (x - 1)

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

= tan (x) + sec^{2} (x) (x - 1) + sin (π x) + π x cos (π x)

What is the derivative of (x-1tan(x)+xsin(pix)) ?
The derivative of (x-1tan(x)+xsin(pix)) is tan(x)+sec^2(x)(x-1)+sin(pix)+pixcos(pix)
What is the first derivative of (x-1tan(x)+xsin(pix)) ?
The first derivative of (x-1tan(x)+xsin(pix)) is tan(x)+sec^2(x)(x-1)+sin(pix)+pixcos(pix)