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$F(X)= X^7+X^3\cdot67$

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Find derivatives using the quotient rule II

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Q.

F(X)= X^7+X^3\cdot67

Apply Power Rule: To find the derivative of $F(X) = X^7 + X^3 \times 67$ , we need to apply the power rule to each term separately. The power rule states that the derivative of $X^n$ is $n \times X^{(n-1)}$ .
Derivative of $X^7$ : First, let's find the derivative of the first term, $X^7$ . Using the power rule, the derivative is $7*X^{(7-1)}$ , which simplifies to $7*X^6$ .
Derivative of $X^3 \times 67$ : Now, let's find the derivative of the second term, $X^3 \times 67$ . Since $67$ is a constant, it remains unchanged when taking the derivative. The derivative of $X^3$ is $3\times X^{(3-1)}$ , which simplifies to $3\times X^2$ . Therefore, the derivative of $X^3 \times 67$ is $67 \times 3\times X^2$ , which simplifies to $201\times X^2$ .
Combine Derivatives: Combining the derivatives of both terms, we get the derivative of $F(X)$ as $F'(X) = 7X^6 + 201X^2$ .

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