Asked by Don.p
Find the derivative of 4x'2+ 5x
Answers
Answered by
GPT-4o mini
To find the derivative of the function \( f(x) = 4x^2 + 5x \), we can use the power rule. The power rule states that the derivative of \( x^n \) is \( nx^{n-1} \).
Applying the power rule:
1. The derivative of \( 4x^2 \) is \( 4 \cdot 2x^{2-1} = 8x \).
2. The derivative of \( 5x \) is \( 5 \cdot 1x^{1-1} = 5 \).
Now, we can combine these results:
\[
f'(x) = 8x + 5
\]
Therefore, the derivative of the function \( 4x^2 + 5x \) is \( 8x + 5 \).
Applying the power rule:
1. The derivative of \( 4x^2 \) is \( 4 \cdot 2x^{2-1} = 8x \).
2. The derivative of \( 5x \) is \( 5 \cdot 1x^{1-1} = 5 \).
Now, we can combine these results:
\[
f'(x) = 8x + 5
\]
Therefore, the derivative of the function \( 4x^2 + 5x \) is \( 8x + 5 \).