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Answer 1 · 2017-02-12T15:00:31

#15/11 x^(4/11) +5x^4 cos x -x^5 sin x#

f(x) is # x^(15/11) +x^5 cos x +e^3#

f(x) is a sum of three functions. Hence derivative of f(x) would be the sum of the derivatives all these three functions. Accordingly,

#d/dx x^(15/11) = 15/11 x^ (4/11) # .. Use of power rule

#d/dx x^5 cos x= 5x^4 cos x + x^5 (-sin x)#... use of product rule

#d/dx e^3 =0#... derivative of a constant is zero

The derivative of f(x) is thus,

#15/11 x^(4/11) +5x^4 cos x -x^5 sin x#