Calculus Examples

Find the Derivative - d/dx 9/(8x^2)
Step 1
Since is constant with respect to , the derivative of with respect to is .
Step 2
Apply basic rules of exponents.
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Step 2.1
Rewrite as .
Step 2.2
Multiply the exponents in .
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Step 2.2.1
Apply the power rule and multiply exponents, .
Step 2.2.2
Multiply by .
Step 3
Differentiate using the Power Rule which states that is where .
Step 4
Simplify terms.
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Step 4.1
Combine and .
Step 4.2
Multiply by .
Step 4.3
Combine and .
Step 4.4
Move to the denominator using the negative exponent rule .
Step 4.5
Cancel the common factor of and .
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Step 4.5.1
Factor out of .
Step 4.5.2
Cancel the common factors.
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Step 4.5.2.1
Factor out of .
Step 4.5.2.2
Cancel the common factor.
Step 4.5.2.3
Rewrite the expression.
Step 4.6
Move the negative in front of the fraction.