What is a Derivative?
The 5 Main Derivative Rules
Special Case Derivatives: Your new multiplication tables
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Example 2: Power Rule Derivative

Differentiate y = 5 x 3 with respect to x.

 

Step 1: Simplify and look for algebraic rewrites.

 

Here the equation is a simplified as we need it, and there are no algebra rewrites.

You always have to check though.

y = 5 x 3

Step 2: Break the problem down into bitesize chunks based upon the + and , and identify the derivative rule for each chunk.

 

Here we have 1 bitesize chunk, 5 x 3 .

 

 

y = 5 x 3

Step 3: Apply derivative rules to each of the chunks you identified in Step 2.

 

          We apply the power rule recipe, Bring the power down Subtract 1 from the power, to the only chunk, 5 x 3 .

The power is 3 . So, we bring that 3 down in front and then subtract 1 from that power.

y = 5 x 3

dy dx = 3 5 x 3 1

dy dx = 15 x 2

dy dx = 15 x 2

 

Final Result:

The derivative of y = 5 x 3  is dy dx = 15 x 2 .

 

Meaning:

          The equation for finding the slope of any tangent line at any x-value of y = 5 x 3   is dy dx = 15 x 2 .

          The instantaneous rate of change for every x-value of y = 5 x 3 , is found by using the derivative equation, dy dx = 15 x 2 .

          The slope of y = 5 x 3 at any single x-value can be found by plugging it into the derivative, dy dx = 15 x 2 .

 

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