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Use The Product Rule To Simplify The Expression Use The Product Rule To Simplify The Expression We use the product rule to simplify the expression where expression is a combination of different kind of variables, numbers and operations like addition, subtraction, multiplication and division. Now, we discuss how product rule simplify different kind of expressions: Combination of algebraic and exponential: If expression is a combination of algebraic and exponential function, then with the help of product rule we can easily solve differentiation of that expression. To simplify with exponents, don't feel like you have to work only from the rules for exponents. It is often simpler to work directly from the definition and meaning of exponents. For instance: Simplify x6 × x5 The rules tell me to add the exponents. But I when I started algebra, I had trouble keeping the rules straight, so I just thought about what exponents mean. Know More About Calculus Worksheets Tutorcircle.com Page No. : 1/4 The " x6 " means "six copies of x multiplied together", and the " x5 " means "five copies of x multiplied together". So if I multiply those two expressions together, I will get eleven copies of x multiplied together. That is: x6 × x5 = (x6)(x5) = (xxxxxx)(xxxxx) (6 times, and then 5 times) = xxxxxxxxxxx (11 times) = x11 Thus: x6 × x5 = x11 Simplify the following expression: The exponent rules tell me to subtract the exponents. But let's suppose that I've forgotten the rules again. The " 68 " means I have eight copies of 6 on top; the " 65 " means I have five copies of 6 underneath. How many extra 6's do I have, and where are they? I have three extra 6's, and they're on top. Then: Note: If you apply the subtraction rule, you'll end up with 53–9 = 5–6, which is mathematically correct, but is almost certainly not the answer they're looking for. Whether or not you've been taught about negative exponents, when they say "simplify", they mean "simplify the expression so it doesn't have any negative or zero powers". Some students will try to get around this minus-sign problem by arbitrarily switching the sign to magically get " 56 " on top (rather than below a "1"), but this is incorrect. Read More About Antiderivative Of Tanx Tutorcircle.com Page No. : 2/4 Examples Simplify the trigonometric expression: syms x simplify(sin(x)^2 + cos(x)^2) Ans = 1 Simplify the expression: syms a b c simplify(exp(c*log(sqrt(a+b)))) ans = (a + b)^(c/2) Simplify the expressions from the matrix: syms x S = [(x^2 + 5*x + 6)/(x + 2), sqrt(16)]; R = simplify(S) R= [ x + 3, 4] Tutorcircle.com Page No. : 3/4 Page No. : 2/3 Thank You TutorCircle.com

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posted: | 5/2/2012 |

language: | English |

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