For the following equation, find f^(')(x). f(x)=8x^(3)+5x+4 Answer: f^(')(x)=

Differentiate 8x^3: We will differentiate each term of the function separately. First, differentiate the term 8x^3. Using the power rule, the derivative of 8x^3 with respect to x is 3*8*x^(3-1) = 24x^2.Differentiate 5x: Next, differentiate the term 5x. The derivative of 5x with respect to x is 5, since the power of x is 1 and 1*x^(1-1) = 1*x^0 = 1.Differentiate constant 4: Finally, differentiate the constant term 4. The derivative of a constant with respect to x is 0, since constants do not change as x changes.Combine derivatives: Now, we combine the derivatives of all the terms to get the derivative of the entire function f(x). f^(')(x) = 24x^2 + 5 + 0Simplify expression: We can simplify the expression by removing the 0, as adding 0 does not change the value. f^(')(x) = 24x^2 + 5 This is the fully simplified form of the derivative of the function f(x).

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Algebra 2

Evaluate expression when a complex numbers and a variable term is given

Full solution

Q. For the following equation, find

f^{\prime}(x)

\newline

f(x)=8 x^{3}+5 x+4

\newline

Answer:

f^{\prime}(x)=

Differentiate $8x^3$ : We will differentiate each term of the function separately. $\newline$ First, differentiate the term $8x^3$ . Using the power rule, the derivative of $8x^3$ with respect to $x$ is $3\cdot8\cdot x^{3-1} = 24x^2$ .
Differentiate $5x$ : Next, differentiate the term $5x$ . The derivative of $5x$ with respect to $x$ is $5$ , since the power of $x$ is $1$ and $1\times x^{1-1} = 1\times x^0 = 1$ .
Differentiate constant $4$ : Finally, differentiate the constant term $4$ . The derivative of a constant with respect to $x$ is $0$ , since constants do not change as $x$ changes.
Combine derivatives: Now, we combine the derivatives of all the terms to get the derivative of the entire function $f(x)$ . $f^{\prime}(x) = 24x^2 + 5 + 0$
Simplify expression: We can simplify the expression by removing the $0$ , as adding $0$ does not change the value. $\newline$ $f^{\prime}(x) = 24x^2 + 5$ $\newline$ This is the fully simplified form of the derivative of the function $f(x)$ .