# Calculate: f(x)=4x^2+sin(6x)-5

## Expression: $f\left( x \right)=4{x}^{2}+\sin\left({6x}\right)-5$

Take the derivative of both sides

$f '\left( x \right)=\frac{ \mathrm{d} }{ \mathrm{d}x} \left( 4{x}^{2}+\sin\left({6x}\right)-5 \right)$

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

$f '\left( x \right)=8x+6\cos\left({6x}\right)$

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