find the derivative of
y = sqrt(9 - 16x)
Use the chain rule. First find the derivative of the sqrt, and multiply that by the derivative of what is contained inside.
Cake.
Use the chain rule. If we have y(x)=sqrt(9-16x) then
y'=d/dx(sqrt(9-16x))*d/dx(9-16x)
The first deriv. is (1/2)(9-16x)^(-1/2), you should be able to finish it.
To find the derivative of y = sqrt(9 - 16x), we will use the chain rule.
The chain rule states that if we have a composition of functions, say g(f(x)), then the derivative with respect to x is given by g'(f(x)) times f'(x).
In our case, we can let g(u) = sqrt(u) and f(x) = 9 - 16x. So our function y = sqrt(9 - 16x) can be written as y = g(f(x)).
Now, we need to find g'(u), the derivative of g(u). We know that the derivative of sqrt(u) is (1/2)u^(-1/2). Therefore, g'(u) = (1/2)u^(-1/2).
Next, we find f'(x), the derivative of f(x) = 9 - 16x. The derivative of a constant with respect to x is zero, so the derivative of 9 with respect to x is zero. The derivative of -16x with respect to x is -16.
Now, we can apply the chain rule to find the derivative of y = sqrt(9 - 16x). Remember that g'(u) = (1/2)u^(-1/2) and f'(x) = -16.
dy/dx = g'(f(x)) * f'(x)
dy/dx = (1/2)(9 - 16x)^(-1/2) * (-16)
Simplifying this expression, we get:
dy/dx = -8 / sqrt(9 - 16x)
Therefore, the derivative of y = sqrt(9 - 16x) is -8 / sqrt(9 - 16x).