More Trig Derivatives Lesson

More Trig Derivatives

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Multiple Choice

Find the derivative of $$f\left(x\right)=\sin^3x\cdot\cos x$$ .

• $$f'\left(x\right)=3\sin^2x\cdot\cos^2x-\sin^4x$$

• $$f'\left(x\right)=3\sin^6x\cdot\cos^2x$$

• $$f'\left(x\right)=-3\sin^3x$$

• $$f'\left(x\right)=\cos^4x-\sin^4x$$

Multiple Choice

Find the derivative of $$f\left(x\right)=\sin^4\ 3x-\cos^4\ 3x$$ .

Hint: You'll need to take out a GCF when you simplify to get the final answer.

• $$f'\left(x\right)=24\sin^33x\cdot\cos^33x$$

• $$f'\left(x\right)=12\sin3x\cdot\cos3x$$

• $$f'\left(x\right)=4\sin^33x+4\cos^33x$$

• $$f'\left(x\right)=12\cos3x-12\sin3x$$

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Exercises

11 & 12

Multiple Choice

Find the derivative of $$f\left(x\right)=\left(1+\cos3x\right)^3$$ .

• $$f'\left(x\right)=3\left(1+\cos3x\right)^2$$

• $$f'\left(x\right)=9\left(1+\cos3x\right)\left(\sin3x\right)$$

• $$f'\left(x\right)=-3\left(1+\cos3x\right)^2\left(\sin3x\right)$$

• $$f'\left(x\right)=-9\left(1+\cos3x\right)^2\left(\sin3x\right)$$

Multiple Choice

What is the equation of the tangent line of $$y=-2\tan x$$ at $$\left(\pi,0\right)$$

• $$y=-2x-\pi$$

• $$y=-x+\pi$$

• $$y=-2x-2\pi$$

• $$y=-x-2\pi$$

Multiple Choice

Find the slope of the tangent line to $$y=\csc x-\cot x$$ when $$x=\frac{\pi}{4}$$ .

• $$m=2-\sqrt[]{2}$$

• $$m=-2\sqrt[]{2}$$

• $$m=0$$

• $$m=2+\sqrt[]{2}$$

Open Ended

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Open Ended

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