Sum Rule

Key Questions

How do you find the derivative of $y = f (x) - g (x)$ $y = f(x) - g(x)$ ?

The derivative for $y = f (x) - g (x)$ $y=f(x)-g(x)$ works the same way as the derivative of $y = f (x) + g (x)$ $y=f(x)+g(x)$ .

$y=f(x)-g(x) => dy/dx=f'(x)-g'(x)$

The quick proof is:
$y=f(x)-g(x)=f(x)+(-1)g(x)$
Using the sum rule and the constant rule:
$dy/dx=f'(x)+(-1)g'(x)=f'(x)-g'(x)$ .

CJ · · Oct 10 2014
How do you find the derivative of $y=f(x)+g(x)$ ?

By Sum Rule,
$y'=f'(x)+g'(x)$

For example, if $y=x^3+e^x$ , then

$y'=(x^3)'+(e^x)'=3x^2+e^x$

Wataru · · Sep 17 2014

Questions

What is the Sum Rule for derivatives?
How do you find the derivative of $y=f(x)+g(x)$ ?
How do you find the derivative of $y = f(x) - g(x)$ ?
What is the derivative of $f(x) = xlnx-lnx^x$ ?
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How do you differentiate $f(x)=1/(x-1)^2+x^3-4/x$ using the sum rule?
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Basic Differentiation Rules

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Power Rule
Chain Rule
Sum Rule
Product Rule
Proof of the Product Rule
Quotient Rule
Implicit Differentiation
Summary of Differentiation Rules
Proof of Quotient Rule

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Sum Rule

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Basic Differentiation Rules