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How do you find the derivative of #y=(2/(x^2))-5x^4#?

Answer 1

Christopher Agresta

#(dy)/(dx)=-4/x^3-20x^3#

We can use here the derivative of #x^n#, which is #nx^(n-1)#

Hence as #y=(2/x^2)-5x^4=2x^(-2)-5x^4#

#(dy)/(dx)=2*(-2)*x^(-2-1)-5*4x^(4-1)#

= #-4x^(-3)-20x^3#

= #-4/x^3-20x^3#

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Answer 2

Samantha Adkison

To find the derivative of the function ( y = \frac{2}{x^2} - 5x^4 ), apply the power rule and the constant multiple rule. The derivative is:

[ y' = \frac{d}{dx}\left(\frac{2}{x^2}\right) - \frac{d}{dx}(5x^4) ]

[ y' = -\frac{4}{x^3} - 20x^3 ]

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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.