Q&A for How to Differentiate Polynomials

Add or subtract "like" terms only, meaning you add or subtract their coefficients. Like terms are those having identical variables. For example, 5x²y³ and 10x²y³ are like terms, but 5x²y³ and 10x²y² are not.

It depends on the degree of the polynomial. If it's linear, simply divide. If it's quadratic, use the formula x = (-b +/-√(b2 - 4ac))/2a. Cubic and quartic equations also have formulas to find the roots (although more complicated). However, it has been proven that there is no general, explicit formula for the roots of equations of degree 5 or higher (see Abel-Ruffini theorem). So you must try to factorize or use trial-and-error to find some roots. If they don't work, then by the above theorem you'll probably never find explicit solutions (unless you use elliptic functions). Of course, if you just want to analyze roots without getting actual values, just examine the graph with differentials.

3² = 9. 2³ = 8. 10(x)^0 = 10(1) = 10. 9 - 8 + 10 = 11.

A negative exponent indicates that the variable (accompanied by a positive rather than negative exponent) is being divided into (rather than multiplied by) the rest of the expression. In contrast, if a variable with a negative exponent appears in the denominator of an expression, that indicates that the variable (accompanied by a positive exponent) is being multiplied by the rest of the expression.

That expression can be written as (2)(x^½)(3)(x^1/3) = (6)(x^5/6) or 6 times the sixth root of x^5.

First, simplify this. Rewrite square root of x^3 as 4x^3/2. Then multiply by 4. Then use the product rule. Keep the first function. 4x^3/2. Multiply by the derivative of the second. Derivative of 4 is 0. Then add. Keep the second function (4) and multiply by the derivative of 4x^3/2 = (3/2)*4x^1/2. You get 6x^1/2, times 4, or 24√x.