For the following equation, find f^(')(x). f(x)=7x^(4)-6x^(2)-1 Answer: f^(')(x)=

Apply Power Rule: To find the derivative of the function f(x) = 7x^(4) - 6x^(2) - 1, we will use the power rule for differentiation. The power rule states that the derivative of x^n with respect to x is n*x^(n-1).Derivative of 7x^(4): Apply the power rule to the first term 7x^(4). The derivative of 7x^(4) with respect to x is 4*7*x^(4-1) = 28x^(3).Derivative of -6x^(2): Apply the power rule to the second term -6x^(2). The derivative of -6x^(2) with respect to x is 2*(-6)*x^(2-1) = -12x.Derivative of constant: The third term -1 is a constant, and the derivative of a constant is 0.Combine derivatives: Combine the derivatives of all terms to get the derivative of the entire function f(x). This gives us f^(')(x) = 28x^(3) - 12x + 0.Simplify final derivative: Simplify the expression by removing the +0 at the end, as it does not affect the value of the derivative. The final derivative is f^(')(x) = 28x^(3) - 12x.

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Q. For the following equation, find

f^{\prime}(x)

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f(x)=7 x^{4}-6 x^{2}-1

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Answer:

f^{\prime}(x)=

Apply Power Rule: To find the derivative of the function $f(x) = 7x^{4} - 6x^{2} - 1$ , we will use the power rule for differentiation. The power rule states that the derivative of $x^n$ with respect to $x$ is $n\cdot x^{(n-1)}$ .
Derivative of $7x^{4}$ : Apply the power rule to the first term $7x^{4}$ . The derivative of $7x^{4}$ with respect to $x$ is $4\cdot7\cdot x^{4-1} = 28x^{3}$ .
Derivative of $-6x^{2}$ : Apply the power rule to the second term $-6x^{2}$ . The derivative of $-6x^{2}$ with respect to $x$ is $2\cdot(-6)\cdot x^{2-1} = -12x$ .
Derivative of constant: The third term $-1$ is a constant, and the derivative of a constant is $0$ .
Combine derivatives: Combine the derivatives of all terms to get the derivative of the entire function $f(x)$ . This gives us $f'(x) = 28x^{3} - 12x + 0$ .
Simplify final derivative: Simplify the expression by removing the $+0$ at the end, as it does not affect the value of the derivative. The final derivative is $f^{\prime}(x) = 28x^{3} - 12x$ .