Answer
$$h'\left( x \right) = - 1.53{x^{ - 0.1}} + {0.9^x}\left( {7\ln 0.9} \right) - \frac{5}{x}$$
Work Step by Step
$$\eqalign{
& h\left( x \right) = - 1.7{x^{0.9}} + 7\left( {{{0.9}^x}} \right) - 5\ln x \cr
& {\text{Calculate the derivative of the function}} \cr
& h'\left( x \right) = \frac{d}{{dx}}\left( { - 1.7{x^{0.9}}} \right) + \frac{d}{{dx}}\left( {7\left( {{{0.9}^x}} \right)} \right) - \frac{d}{{dx}}\left( {5\ln x} \right) \cr
& {\text{Drop out the constants}} \cr
& h'\left( x \right) = - 1.7\frac{d}{{dx}}\left( {{x^{0.9}}} \right) + 7\frac{d}{{dx}}\left( {{{0.9}^x}} \right) - 5\frac{d}{{dx}}\left( {\ln x} \right) \cr
& {\text{Compute derivatives}}{\text{, }} \cr
& h'\left( x \right) = - 1.7\left( {0.9{x^{ - 0.1}}} \right) + 7\left( {{{0.9}^x}\ln 0.9} \right) - 5\left( {\frac{1}{x}} \right) \cr
& h'\left( x \right) = - 1.53{x^{ - 0.1}} + {0.9^x}\left( {7\ln 0.9} \right) - \frac{5}{x} \cr} $$
