What is the derivative of #(1-x^2)/(x^3)#?

Answer 1

Luke Alvarez

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

Split up the fraction and rewrite it with negative exponents:

#(1-x^2)/x^3=1/x^3-x^2/x^3=x^-3-x^-1#

Now, differentiate #x^-3-x^-1# using the power rule, which states that the derivative of #x^n=nx^(n-1)#. Thus:

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

#=-3x^-4+x^-2#

This is a valid final answer, but we can also write it without negative exponents by multiplying it by #x^4/x^4#:

#(x^4(-3x^-4+x^-2))/x^4=(-3+x^2)/x^4=(x^2-3)/x^4#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Emilia Aguilar

To find the derivative of (1-x^2)/(x^3), you can use the quotient rule. The derivative of the numerator is -2x, and the derivative of the denominator is 3x^2. Applying the quotient rule, you get: ((-2x)(x^3) - (1-x^2)(3x^2))/(x^3)^2

Simplify this expression to get the final derivative.

By signing up, you agree to our Terms of Service and Privacy Policy

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.