Differentiate y=13x^2-5x+8
Well, let's put on our math caps and get to work!
To differentiate the function y = 13x^2 - 5x + 8, we can use the power rule and the constant rule. The power rule states that the derivative of x^n is nx^(n - 1), and the constant rule states that the derivative of a constant is 0.
So, let's differentiate term by term:
The derivative of 13x^2 is 26x because 2 * 13 = 26x^(2 - 1).
The derivative of -5x is -5 because 1 * -5 = -5x^(1 - 1), which simplifies to -5.
The derivative of 8 is 0 because it's just a constant.
Now let's put it all together:
dy/dx = 26x - 5 + 0
Simplifying, we get:
dy/dx = 26x - 5
And there you have it! The derivative of y = 13x^2 - 5x + 8 is dy/dx = 26x - 5.
I hope that puts a smile on your face! If not, well, I guess math can be a tough act to follow sometimes.
To differentiate the function y = 13x^2 - 5x + 8, we will use the power rule and the constant rule in calculus.
Step 1: Apply the power rule:
Differentiating the term 13x^2 with respect to x, we bring down the exponent 2 as a coefficient and then reduce the exponent by 1, resulting in 26x.
So, the derivative of 13x^2 is 26x.
Step 2: Apply the power rule again:
Differentiating the term -5x with respect to x, we bring down the coefficient -5, and since x has an implied exponent of 1, we reduce the exponent by 1 as well, resulting in -5.
So, the derivative of -5x is -5.
Step 3: Apply the constant rule:
The derivative of any constant term, such as 8, with respect to x is 0. Therefore, this term does not contribute to the derivative.
So, the derivative of 8 is 0.
Combining all the derivatives obtained above, the derivative of y = 13x^2 - 5x + 8 is:
dy/dx = 26x - 5
To differentiate the given function y = 13x^2 - 5x + 8, we will apply the power rule and the constant rule of differentiation. The power rule states that the derivative of x^n, where n is a constant, is given by nx^(n-1).
Let's differentiate each term one by one and then combine the results:
1. Differentiating the term 13x^2:
Applying the power rule, we get: derivative of 13x^2 = 2 * 13x^(2-1) = 26x.
2. Differentiating the term -5x:
Applying the power rule, we get: derivative of -5x = 1 * -5x^(1-1) = -5.
3. Differentiating the constant term 8:
Since the derivative of a constant is zero, the derivative of 8 is 0.
Now, combining the derivatives of each term, we get:
dy/dx = 26x - 5 + 0
Simplifying further, we have:
dy/dx = 26x - 5
Therefore, the derivative of y = 13x^2 - 5x + 8 with respect to x is dy/dx = 26x - 5.