Calculus Examples

Find the Derivative - d/dx f(x)=(7x)/(2^x)
Step 1
Since is constant with respect to , the derivative of with respect to is .
Step 2
Differentiate using the Quotient Rule which states that is where and .
Step 3
Differentiate using the Power Rule.
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Step 3.1
Multiply the exponents in .
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Step 3.1.1
Apply the power rule and multiply exponents, .
Step 3.1.2
Move to the left of .
Step 3.2
Differentiate using the Power Rule which states that is where .
Step 3.3
Multiply by .
Step 4
Differentiate using the Exponential Rule which states that is where =.
Step 5
Combine and .
Step 6
Simplify.
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Step 6.1
Apply the distributive property.
Step 6.2
Simplify the numerator.
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Step 6.2.1
Simplify each term.
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Step 6.2.1.1
Multiply .
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Step 6.2.1.1.1
Multiply by .
Step 6.2.1.1.2
Simplify by moving inside the logarithm.
Step 6.2.1.2
Rewrite using the commutative property of multiplication.
Step 6.2.1.3
Raise to the power of .
Step 6.2.2
Reorder factors in .
Step 6.3
Reorder terms.
Step 6.4
Factor out of .
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Step 6.4.1
Factor out of .
Step 6.4.2
Factor out of .
Step 6.4.3
Factor out of .
Step 6.5
Cancel the common factor of and .
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Step 6.5.1
Factor out of .
Step 6.5.2
Cancel the common factors.
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Step 6.5.2.1
Multiply by .
Step 6.5.2.2
Cancel the common factor.
Step 6.5.2.3
Rewrite the expression.
Step 6.5.2.4
Divide by .
Step 6.6
Apply the distributive property.
Step 6.7
Rewrite using the commutative property of multiplication.
Step 6.8
Move to the left of .
Step 6.9
Reorder factors in .