Derivative problem order of opeartions

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In summary, the problem involves finding the limit of a function with a derivative. The equation is simplified using order of operations, with the numerator being 75-(10+20*h+10*h^2)+(1+h)-66 and the simplified version being 75-10-20*h-10*h^2+1+h-66. The author explains how to combine constants and equal powers of h to find the solution.
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Press90
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Derivative problem "order of opeartions"

Homework Statement



= lim [75-(10+20h+10h"squared") + (1+h)] - (66)
h-0 h

= lim -19h - 10h"squared"
h-0 h

Homework Equations


So sorry, as this is a simple understanding; which i don't have. But how did the author arrive to the second part of the equation? I forget the order of operations.


The Attempt at a Solution


 
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The numerator is 75-(10+20*h+10*h^2)+(1+h)-66. That's the same as 75-10-20*h-10*h^2+1+h-66. Negate the terms in parentheses if there is minus outside, leave them alone if there is a plus outside. Now just combine constants and equal powers of h. Is that your question?
 

What is the derivative?

The derivative is a mathematical concept that represents the instantaneous rate of change of a function. It is essentially the slope of a function at a specific point.

What is the order of operations for solving derivative problems?

The order of operations for solving derivative problems is as follows: 1. Simplify any expressions inside parentheses. 2. Apply the power rule (if necessary). 3. Apply the product rule (if necessary). 4. Apply the quotient rule (if necessary). 5. Apply the chain rule (if necessary). 6. Simplify the final expression.

What is the power rule?

The power rule is a formula used to find the derivative of a function raised to a power. It states that the derivative of x^n is n*x^(n-1), where n is any real number.

What is the product rule?

The product rule is a formula used to find the derivative of a product of two functions. It states that the derivative of f(x)*g(x) is f'(x)*g(x) + f(x)*g'(x), where f'(x) and g'(x) are the derivatives of the individual functions.

What is the chain rule?

The chain rule is a formula used to find the derivative of a composite function. It states that the derivative of f(g(x)) is f'(g(x))*g'(x), where f'(x) is the derivative of the outer function and g'(x) is the derivative of the inner function.

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