$f '\left( x \right)=\frac{ \mathrm{d} }{ \mathrm{d}x} \left( 4{x}^{2}+\sin\left({6x}\right)-5 \right)$
Use differentiation rule $\frac{ \mathrm{d} }{ \mathrm{d}x} \left( f+g \right)=\frac{ \mathrm{d} }{ \mathrm{d}x} \left( f \right)+\frac{ \mathrm{d} }{ \mathrm{d}x} \left( g \right)$$f '\left( x \right)=\frac{ \mathrm{d} }{ \mathrm{d}x} \left( 4{x}^{2} \right)+\frac{ \mathrm{d} }{ \mathrm{d}x} \left( \sin\left({6x}\right) \right)-\frac{ \mathrm{d} }{ \mathrm{d}x} \left( 5 \right)$
Find the derivative$f '\left( x \right)=4 \times 2x+\frac{ \mathrm{d} }{ \mathrm{d}x} \left( \sin\left({6x}\right) \right)-\frac{ \mathrm{d} }{ \mathrm{d}x} \left( 5 \right)$
Find the derivative of the composite function$f '\left( x \right)=4 \times 2x+\cos\left({6x}\right) \times 6-\frac{ \mathrm{d} }{ \mathrm{d}x} \left( 5 \right)$
Find the derivative$f '\left( x \right)=4 \times 2x+\cos\left({6x}\right) \times 6-0$
Simplify the expression$f '\left( x \right)=8x+6\cos\left({6x}\right)$