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How do you find the derivative of # cos(1-2x)^2#?

Answer 1

Elijah Abram

#4(1-2x)sin(1-2x)^2#

#"differentiate using the "color(blue)"chain rule"#

#"given "y=f(g(x))" then"#

#dy/dx=f'(g(x))xxg'(x)larrcolor(blue)"chain rule"#

#rArrd/dx(cos(1-2x)^2)#

#=-sin(1-2x)^2xxd/dx((1-2x)^2)#

#=-sin(1-2x)^2xx2(1-2x)xxd/dx(1-2x)#

#=-sin(1-2x)^2xx2(1-2x)xx-2#

#=4(1-2x)sin(1-2x)^2#

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Answer 2

Isaiah Allen

To find the derivative of ( \cos(1-2x)^2 ), you can use the chain rule. The derivative can be calculated as follows:

[ \frac{d}{dx}[\cos(1-2x)^2] = -2 \sin(1-2x) \cdot \frac{d}{dx}(1-2x) ]

Now, differentiate ( 1-2x ) with respect to ( x ):

[ \frac{d}{dx}(1-2x) = -2 ]

Putting it back into the expression:

[ \frac{d}{dx}[\cos(1-2x)^2] = -2 \sin(1-2x) \cdot (-2) ]

[ = 4 \sin(1-2x) ]

So, the derivative of ( \cos(1-2x)^2 ) with respect to ( x ) is ( 4 \sin(1-2x) ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.