How do you differentiate #f(x)=1/x+5sinx#?

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Answer 1 · 2017-02-07T19:12:43

#d/dx (1/x+5sinx) =-1/x^2+5cosx#

Using the linearity of differentiation we have:

#d/dx (1/x+5sinx) = d/dx (1/x) + 5 d/dx(sinx)#

The first term can be differentiated using the power rule:

#d/dx (1/x) = d/dx (x^(-1)) = (-1)x^(-2) = -1/x^2#

while the second term is the known derivative of a trigonometric function:

#d/dx(sinx) = cosx#

And in conclusion:

#d/dx (1/x+5sinx) =-1/x^2+5cosx#