Find the derivative of -8x²-5x+13
The derivative of -8x²-5x+13 is:
(d/dx)(-8x²) + (d/dx)(-5x) + (d/dx)(13)
Using the power rule, the derivative of -8x² is -16x.
Using the power rule, the derivative of -5x is -5.
The derivative of a constant (in this case, 13) is 0.
So, the derivative of -8x²-5x+13 is -16x - 5 + 0,
which simplifies to -16x - 5.
To find the derivative of the given function, we can apply the power rule for derivatives. The power rule states that the derivative of x to the power of n, where n is a constant, is given by nx^(n-1).
Let's apply the power rule to derive each term of the function:
1) The derivative of -8x^2 is calculated as follows:
- derivative of -8 is 0 (since it's a constant)
- derivative of x^2 is 2x (applying the power rule)
Therefore, the derivative of -8x^2 is 0x^2 + 2x(derivative of -8) which simplifies to -16x.
2) The derivative of -5x is calculated as follows:
- derivative of -5 is 0 (since it's a constant)
- derivative of x is 1 (applying the power rule)
Therefore, the derivative of -5x is 0x + 1(derivative of -5) which simplifies to -5.
3) The derivative of 13 is 0 (since it's a constant).
Therefore, the derivative of the function -8x^2 - 5x + 13 is -16x - 5.