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${:[=x^(2)+4],[=(g+h)(x)]:} {:[h(x)=x^(2)+x],[g(x)=3x+5],[" Find "(h*g)(x)]:}$

$\begin{array}{l} =x^{2}+4 \\ =(g+h)(x) \end{array}$ $\newline$ $9$ . $\newline$ $\begin{array}{l} h(x)=x^{2}+x \\ g(x)=3 x+5 \\ \text { Find }(h \cdot g)(x) \end{array}$

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Find higher derivatives of rational and radical functions

Full solution

Q.

\begin{array}{l} =x^{2}+4 \\ =(g+h)(x) \end{array}

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9

.

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

Identify functions: Identify the functions to be multiplied. $\newline$ We are given two functions: $\newline$ $h(x) = x^2 + x$ $\newline$ $g(x) = 3x + 5$ $\newline$ We need to find the product of these two functions, which is denoted as $(h*g)(x)$ .
Multiply functions: Multiply the functions using the distributive property (also known as the FOIL method for binomials). $\newline$ $(h*g)(x) = (x^2 + x) \times (3x + 5)$ $\newline$ To multiply these, we distribute each term in the first function by each term in the second function.
Perform multiplication: Perform the multiplication. $\newline$ $(h*g)(x) = x^2 \cdot 3x + x^2 \cdot 5 + x \cdot 3x + x \cdot 5$
Simplify expression: Simplify the expression by combining like terms and performing the multiplication. $\newline$ $(h*g)(x) = 3x^3 + 5x^2 + 3x^2 + 5x$ $\newline$ $(h*g)(x) = 3x^3 + (5x^2 + 3x^2) + 5x$ $\newline$ $(h*g)(x) = 3x^3 + 8x^2 + 5x$

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