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{:[h(x)=x^(2)+x],[g(x)=3x+5],[" Find "(h*g)(x)]:}

h(x)=x2+xg(x)=3x+5 Find (h⋅g)(x)\begin{array}{l}h(x)=x^{2}+x \\ g(x)=3 x+5 \\ \text{ Find }(h \cdot g)(x)\end{array}

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Find higher derivatives of rational and radical functionsright chevron icon

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Q. h(x)=x2+xg(x)=3x+5 Find (h⋅g)(x)\begin{array}{l}h(x)=x^{2}+x \\ g(x)=3 x+5 \\ \text{ Find }(h \cdot g)(x)\end{array}
  1. Identify functions: Identify the functions to be multiplied.\newlineWe are given two functions:\newlineh(x)=x2+xh(x) = x^2 + x\newlineg(x)=3x+5g(x) = 3x + 5\newlineWe need to find the product of these two functions, which is denoted as (h∗g)(x)(h*g)(x).
  2. Multiply functions: Multiply the functions using the distributive property (also known as the FOIL method for binomials).\newline(h∗g)(x)=(x2+x)×(3x+5)(h*g)(x) = (x^2 + x) \times (3x + 5)\newlineTo multiply these, we distribute each term in the first function by each term in the second function.
  3. Perform multiplication: Perform the multiplication.\newline(h∗g)(x)=x2⋅3x+x2⋅5+x⋅3x+x⋅5(h*g)(x) = x^2 \cdot 3x + x^2 \cdot 5 + x \cdot 3x + x \cdot 5
  4. Simplify expression: Simplify the expression by combining like terms and performing the multiplication.\newline(h∗g)(x)=3x3+5x2+3x2+5x(h*g)(x) = 3x^3 + 5x^2 + 3x^2 + 5x\newline(h∗g)(x)=3x3+(5x2+3x2)+5x(h*g)(x) = 3x^3 + (5x^2 + 3x^2) + 5x\newline(h∗g)(x)=3x3+8x2+5x(h*g)(x) = 3x^3 + 8x^2 + 5x

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