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How do you find the derivative of # 2/(5x+1)^2#?

Answer 1

Christopher Allers

#(dy)/(dx)=-20/(5x+1)^3#

#y=2/(5x+1)^2=2(5x+1)^-2#

Let #u=5x+1#,

#d/(du)2u^-2=-4u^-3=-4(5x+1)^-3#

#d/(dx)5x+1=5#

Using chain rule, #(dy)/(dx)=(dy)/(du)*(du)/(dx)#,

#(dy)/(dx)=-4(5x+1)^-3*5#

#=-20(5x+1)^-3#

#=-20/(5x+1)^3#

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Answer 2

Christopher Allers

To find the derivative of ( \frac{2}{{(5x+1)}^2} ), you can use the chain rule and the power rule for differentiation. Here's the step-by-step process:

Identify the function: ( f(x) = \frac{2}{{(5x+1)}^2} ).
Rewrite the function using negative exponents: ( f(x) = 2(5x+1)^{-2} ).
Apply the power rule: ( f'(x) = -2 \cdot 2(5x+1)^{-3} ).
Simplify: ( f'(x) = \frac{-4}{{(5x+1)}^3} ).

So, the derivative of ( \frac{2}{{(5x+1)}^2} ) with respect to ( x ) is ( \frac{-4}{{(5x+1)}^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.