Calculus Examples

Find the Derivative - d/dx y=1/(x^8)
y=1x8
Step 1
Apply basic rules of exponents.
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Step 1.1
Rewrite 1x8 as (x8)-1.
ddx[(x8)-1]
Step 1.2
Multiply the exponents in (x8)-1.
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Step 1.2.1
Apply the power rule and multiply exponents, (am)n=amn.
ddx[x8-1]
Step 1.2.2
Multiply 8 by -1.
ddx[x-8]
ddx[x-8]
ddx[x-8]
Step 2
Differentiate using the Power Rule which states that ddx[xn] is nxn-1 where n=-8.
-8x-9
Step 3
Simplify.
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Step 3.1
Rewrite the expression using the negative exponent rule b-n=1bn.
-81x9
Step 3.2
Combine terms.
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Step 3.2.1
Combine -8 and 1x9.
-8x9
Step 3.2.2
Move the negative in front of the fraction.
-8x9
-8x9
-8x9
 [x2  12  π  xdx ]