How do you find the derivative of #f(x)=ax+b#?

Answer 1

#f^'(x)=a#

#f(x)=ax+b#

Take derivative on both sides:

#d/dx(f(x))=d/dx(ax+b)#

Apply the sum/difference rule for derivative which is stated as:

#d/dx(f+g)=d/dx(f)+d/dx(g)#

So that we will have:

#f^'(x)=d/dx(ax)+d/dx(b)#

Remember the derivative of a constant is zero, so that we will have:

#f^'(x)=d/dx(ax)+0#
Take the constant out by applying #d/dx(a*f)=a*d/dx(f)#
#f^'(x)=a*d/dx(x)#
Apply the common derivative rule #d/dx(x)=1#
#f^'(x)=a*1#
#f^'(x)=a#
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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.

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.

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.

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.

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