Trig Diff Example

[Jason76]

\(\displaystyle f(x) = \sin(x) + \dfrac{5}{3} \cot(x)\)

\(\displaystyle f'(x) = \dfrac{d}{dx} \sin(x) + \dfrac{d}{dx} \dfrac{5}{3} \cot(x)\)

\(\displaystyle f'(x) = \dfrac{d}{dx} \sin(x) + \dfrac{5}{3} [\dfrac{d}{dx} \cot(x)]\)

\(\displaystyle f'(x) = \cos(x) + \dfrac{5}{3}(-csc^{2}(x))\) - Should this step be left out? Since the negative sign in front of \(\displaystyle \csc^{2}(x)\) looks like a minus sign.

\(\displaystyle f'(x) = \cos(x) + [-\dfrac{5}{3} csc^{2}(x)]\)

\(\displaystyle f'(x) = \cos(x) - \dfrac{5}{3} csc^{2}(x)\)

 

[fcabanski]

It's best to write out each step, so you don't make mistakes. "Should this step be left out? Since the negative sign in front of [FONT=MathJax_Main]csc[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main])[/FONT] looks like a minus sign." The inclusion of the () makes it clear it is multiplication rather than subtraction.

Your answer is correct. You can check your answers at wolframalpha.com. Type "derivative f(x)" where f(x) is the equation. It's a good way to check your answers.

 

[Jason76]

Do these two lines look ok :?:

\(\displaystyle f'(x) = \dfrac{d}{dx} \sin(x) + \dfrac{d}{dx} \dfrac{5}{3} \cot(x)\)

\(\displaystyle f'(x) = \dfrac{d}{dx} \sin(x) + \dfrac{5}{3} [\dfrac{d}{dx} \cot(x)]\)

It's best to write out each step, so you don't make mistakes. "Should this step be left out? Since the negative sign in front of [FONT=MathJax_Main]csc[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main])[/FONT] looks like a minus sign." The inclusion of the () makes it clear it is multiplication rather than subtraction.

Your answer is correct. You can check your answers at wolframalpha.com. Type "derivative f(x)" where f(x) is the equation. It's a good way to check your answers.

Thanks.

 

[fcabanski]

Do these two lines look ok :?:

\(\displaystyle f'(x) = \dfrac{d}{dx} \sin(x) + \dfrac{d}{dx} \dfrac{5}{3} \cot(x)\)

\(\displaystyle f'(x) = \dfrac{d}{dx} \sin(x) + \dfrac{5}{3} [\dfrac{d}{dx} \cot(x)]\)



Thanks.

Yes, that is correct step by step.

 

[Deleted member 4993]

Do these two lines look ok :?:

\(\displaystyle f'(x) = \dfrac{d}{dx} \sin(x) + \dfrac{d}{dx} \dfrac{5}{3} \cot(x)\) ......... better to write it as f'(x) = \(\displaystyle \dfrac{d}{dx} \sin(x) + \displaystyle \dfrac{d}{dx} \left [\dfrac{5}{3} \cot(x) \right ]\)

\(\displaystyle f'(x) = \dfrac{d}{dx} \sin(x) + \dfrac{5}{3} [\dfrac{d}{dx} \cot(x)]\)



Thanks.

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