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 expressiond (x.ex) = x. d (ex) + ex.d (x) dx dx dx = x.ex + ex.1 = ex(x+1) Know More About Antiderivative of a x
Combination of algebraic and trigonometric: If expression is a combination of algebraic and trigonometric function, thend (x2.sin x) = x2. d (sin x) + sinx.d (x2) dx dx dx = x2.(cos x) + sin x .(2x) = x(x.cos x + 2.sin x) Combination of algebraic and logarithm: If expression is a combination of algebraic and logarithm function, thend (x.ln x) = x. d (ln x) + ln x.d (x) dx dx dx = x.(1) + ln x.(1) x = 1+ ln x Combination of trigonometric: If expression is a combination of two trigonometric functions, thend (sin x. cosx) = sin x. d (cos x) + cos x.d (sin x) Learn More About Antiderivative Trig Functions
dx dx dx = sin x.(-sin2x) + cos x.(cos x) = cos2x – sin2x = cos2x
Combination of trigonometric and exponential: If expression is a combination of trigonometric and exponential function, thend (sin x.ex) = sin x. d (ex) + ex. d (sin x) dx dx dx = sin x. (ex) + ex.(cos x) = ex (sinx + cos x) These are different expressions which we simplify by product rule.
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