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How do you differentiate #sqrt(2x^3 - 3x- 4)#?

Answer 1

Emilia Aguilar

#(3(2x^2-1))/(2sqrt(2x^3-3x-4))#

This can be rewritten as #(2x^3-3x-4)^(1/2)#.

According to the chain rule, #d/dx(u^(1/2))=1/2u^(-1/2)*(du)/dx#.

Thus,

#d/dx(2x^3-3x-4)^(1/2)=1/2(2x^3-3x-4)^(-1/2)d/dx(2x^3-3x-4)#

#=>1/(2sqrt(2x^3-3x-4))*(6x^2-3)#

#=>(3(2x^2-1))/(2sqrt(2x^3-3x-4))#

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Answer 2

Isabella Ackerman

To differentiate sqrt(2x^3 - 3x - 4), you can use the chain rule. The derivative of sqrt(u) with respect to x is (1/2) * (u^(-1/2)) * du/dx. Here, u = 2x^3 - 3x - 4. Now, differentiate u with respect to x, then substitute it into the chain rule formula, and simplify. The result will be the derivative of sqrt(2x^3 - 3x - 4) with respect to x.

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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.