find dq/dp.q=(5p^2+2p)-3/2 use impliict differentiation to find dq/dp
Why did the chicken go to the math party? Because it wanted to find its derivative, of course!
To find dq/dp for the equation q = (5p^2 + 2p) - (3/2), we'll use implicit differentiation, which is like trying to solve a mystery. So, let's put on our detective hats and get solving!
First, let's start by differentiating both sides of the equation with respect to p. On the left side, we'll get dq/dp (that's our mystery derivative), and on the right side, we'll differentiate each term one by one.
Differentiating (5p^2) with respect to p, we get 10p. Differentiating (2p) with respect to p, we get 2. And differentiating (3/2) with respect to p, we get 0 (because a constant doesn't change with p).
So now our differentiated equation looks like this: dq/dp = 10p + 2 - 0.
Simplifying further: dq/dp = 10p + 2.
And there you have it! We cracked the case and found the derivative dq/dp using implicit differentiation. Keep up the detective work!
To find dq/dp using implicit differentiation, we'll differentiate both sides of the equation with respect to p. Let's start with the given equation:
q = (5p^2 + 2p) - 3/2
First, let's differentiate the left side of the equation with respect to p. Since q is a function of p, we'll treat q as a constant for the purposes of differentiation:
d/dp (q) = d/dp (q)
Now, let's differentiate the right side of the equation with respect to p. We'll apply the chain rule and multiply the derivative of the outer function (5p^2 + 2p - 3/2) by the derivative of the inner function (with respect to p).
For the outer function, we have:
d/dp (5p^2 + 2p - 3/2)
To differentiate each term separately:
d/dp (5p^2) = 10p
d/dp (2p) = 2
d/dp (-3/2) = 0 (since it's a constant)
Now we can rewrite the derivative of the outer function:
d/dp (5p^2 + 2p - 3/2) = 10p + 2
So, the equation becomes:
d/dp (q) = 10p + 2
Now, we have the derivative of q with respect to p, which is dq/dp = 10p + 2.