Calculus Examples

Find dy/dx v(y)=x-3/95x^3
Step 1
Multiply by .
Step 2
Differentiate both sides of the equation.
Step 3
Differentiate the left side of the equation.
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Step 3.1
Since is constant with respect to , the derivative of with respect to is .
Step 3.2
Rewrite as .
Step 4
Differentiate the right side of the equation.
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Step 4.1
Differentiate.
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Step 4.1.1
By the Sum Rule, the derivative of with respect to is .
Step 4.1.2
Differentiate using the Power Rule which states that is where .
Step 4.2
Evaluate .
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Step 4.2.1
Since is constant with respect to , the derivative of with respect to is .
Step 4.2.2
Differentiate using the Power Rule which states that is where .
Step 4.2.3
Multiply by .
Step 4.2.4
Combine and .
Step 4.2.5
Multiply by .
Step 4.2.6
Combine and .
Step 4.2.7
Move the negative in front of the fraction.
Step 4.3
Reorder terms.
Step 5
Reform the equation by setting the left side equal to the right side.
Step 6
Solve for .
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Step 6.1
Multiply by .
Step 6.2
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 6.3
Simplify .
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Step 6.3.1
Write as a fraction with a common denominator.
Step 6.3.2
Combine the numerators over the common denominator.
Step 6.3.3
Rewrite as .
Step 6.3.4
Multiply by .
Step 6.3.5
Combine and simplify the denominator.
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Step 6.3.5.1
Multiply by .
Step 6.3.5.2
Raise to the power of .
Step 6.3.5.3
Raise to the power of .
Step 6.3.5.4
Use the power rule to combine exponents.
Step 6.3.5.5
Add and .
Step 6.3.5.6
Rewrite as .
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Step 6.3.5.6.1
Use to rewrite as .
Step 6.3.5.6.2
Apply the power rule and multiply exponents, .
Step 6.3.5.6.3
Combine and .
Step 6.3.5.6.4
Cancel the common factor of .
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Step 6.3.5.6.4.1
Cancel the common factor.
Step 6.3.5.6.4.2
Rewrite the expression.
Step 6.3.5.6.5
Evaluate the exponent.
Step 6.3.6
Combine using the product rule for radicals.
Step 6.3.7
Reorder factors in .
Step 6.4
The complete solution is the result of both the positive and negative portions of the solution.
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Step 6.4.1
First, use the positive value of the to find the first solution.
Step 6.4.2
Next, use the negative value of the to find the second solution.
Step 6.4.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 7
Replace with .