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\[\frac{d}{dx} \cos{(\ln{({x}^{3})})}\]
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dif(cos(ln(x^3)))
differentiate cos(ln(x^3))
\frac{d}{dx} \cos{(\ln{({x}^{3})})}
1
Use
Chain Rule
on \(\frac{d}{dx} \cos{(\ln{({x}^{3})})}\). Let \(u=\ln{({x}^{3})}\). Use
Trigonometric Differentiation
: the derivative of \(\cos{u}\) is \(-\sin{u}\).
\[-\sin{(\ln{({x}^{3})})}(\frac{d}{dx} \ln{({x}^{3})})\]
2
Use
Chain Rule
on \(\frac{d}{dx} \ln{({x}^{3})}\). Let \(u={x}^{3}\). The derivative of \(\ln{u}\) is \(\frac{1}{u}\).
\[-\sin{(\ln{({x}^{3})})}\times \frac{1}{{x}^{3}}(\frac{d}{dx} {x}^{3})\]
3
Use
Power Rule
: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[-\frac{3\sin{(\ln{({x}^{3})})}}{x}\]
Done
-(3*sin(ln(x^3)))/x
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