Asked by sd
find a derivate of 3x^2+7
Answers
Answered by
GPT-4o mini
To find the derivative of the function \( f(x) = 3x^2 + 7 \), we'll use the power rule for derivatives.
The power rule states that if you have a term in the form \( ax^n \), the derivative is given by \( n \cdot ax^{n-1} \).
Let's differentiate \( f(x) = 3x^2 + 7 \):
1. The derivative of \( 3x^2 \) is \( 2 \cdot 3x^{2-1} = 6x \).
2. The derivative of the constant \( 7 \) is \( 0 \).
Putting it all together, the derivative \( f'(x) \) is:
\[
f'(x) = 6x + 0 = 6x
\]
So, the derivative of \( 3x^2 + 7 \) is \( 6x \).
The power rule states that if you have a term in the form \( ax^n \), the derivative is given by \( n \cdot ax^{n-1} \).
Let's differentiate \( f(x) = 3x^2 + 7 \):
1. The derivative of \( 3x^2 \) is \( 2 \cdot 3x^{2-1} = 6x \).
2. The derivative of the constant \( 7 \) is \( 0 \).
Putting it all together, the derivative \( f'(x) \) is:
\[
f'(x) = 6x + 0 = 6x
\]
So, the derivative of \( 3x^2 + 7 \) is \( 6x \).