Q. For the following equation, find f′(x).f(x)=−2x2+6x+3Answer: f′(x)=
Apply Power Rule: To find the derivative of the function f(x)=−2x2+6x+3, we will use the power rule for differentiation. The power rule states that the derivative of xn with respect to x is n⋅x(n−1).
Differentiate −2x2: Applying the power rule to the first term −2x2, we differentiate it as follows:The derivative of −2x2 with respect to x is −2×2x2−1=−4x.
Differentiate 6x: Next, we apply the power rule to the second term 6x, which is a first-degree polynomial. The derivative of 6x with respect to x is 6×1x(1−1)=6.
Differentiate constant: The third term is a constant, 3. The derivative of a constant with respect to x is 0.
Combine derivatives: Now, we combine the derivatives of all three terms to find the derivative of the entire function f(x):f′(x)=−4x+6+0.
Simplify final answer: Simplify the derivative to get the final answer: f′(x)=−4x+6.
More problems from Composition of linear and quadratic functions: find a value