what is tangent line at the point below?

Question

An equation of the tangent line to the curve
y=f(x)=x(7 cosx- 2 sinx)

at the point (3 p,f(3 p) is ???/

Answer 1

the slope is given by f'(x) = x (-7sinx -2cosx) + 7cosx -2sinx
f'(3p) = 3p ( -7sin3p -2 cos3p ) + 7 cos3p -2sin3p

so the equation of the tangent line is:
y-f(3p) = [3p ( -7sin3p -2 cos3p ) + 7 cos3p -2sin3p](x-3p)

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