# Find the Derivative minus d First, divide dx y equals minus(x to the power of two) divide sixteen plus two divide x minus x to the power of(three divide two) plus one divide(three x to the power of two) plus x divide three

Find the Derivative - d/dx y=-(x^2)/16+2/x-x^(3/2)+1/(3x^2)+x/3
By the Sum Rule, the derivative of with respect to is .
Evaluate .
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
First, First, multiply by .
Combine and .
The common factor should be canceled of and .
Factor out of .
The common factors should be canceled.
Factor out of .
Cancel the common factor.
Reformulate the expression.
Put the negative in front of the fraction.
Evaluate .
Since is constant with respect to , the derivative of with respect to is .
Should be rewritten as .
Differentiate using the Power Rule which states that is where .
Multiply by .
Evaluate .
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
To write as a fraction with a common denominator, multiply by .
Combine and .
Add numerators over the common denominator.
Clarify the numerator.
Multiply by .
Subtract from .
Combine and .
Evaluate .
Since is constant with respect to , the derivative of with respect to is .
Rewrite as .
Differentiate using the chain rule, which states that is where and .
To apply the Chain Rule, set as .
Differentiate using the Power Rule which states that is where .
Replace all occurrences of with .
Differentiate using the Power Rule which states that is where .
Multiply the exponents in .
Apply the power rule when multiplying the exponents, .
Multiply by .
Multiply by .
Raise to the power of .
Use the power rule to Add exponents.
Subtract from .
Combine and .
Combine and .
Move to the denominator using the negative exponent rule .
Move the negative in front of the fraction.
Evaluate .
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Multiply by .
Reformulate the expression applying the negative exponent law .
Simplify.
Combine terms.
Combine and .
Move the negative in front of the fraction.
Shift terms.
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