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a.
f(x)=3x^(2)+4x+1

a. $f(x)=3 x^{2}+4 x+1$

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Add and subtract polynomials

Full solution

Q. a.

f(x)=3 x^{2}+4 x+1

Identify function: Identify the function to differentiate. $f(x)=3x^{2}+4x+1$
Apply power rule: Apply the power rule to the first term. $\newline$ Derivative of $3x^{2}$ is $6x$ .
Combine derivatives: Apply the power rule to the second term. $\newline$ Derivative of $4x$ is $4$ .
Simplify derivative: The constant term's derivative is $0$ . Derivative of $1$ is $0$ .
Simplify derivative: The constant term's derivative is $0$ . Derivative of $1$ is $0$ . Combine the derivatives of each term. $f'(x) = 6x + 4 + 0$
Simplify derivative: The constant term's derivative is $0$ . Derivative of $1$ is $0$ . Combine the derivatives of each term. $f'(x) = 6x + 4 + 0$ Simplify the derivative. $f'(x) = 6x + 4$

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