First of all, recall that y is a product of function of x. We have three factors:
![f(x)=x^2,\quad g(x)=e^{3x},\quad h(x)=\sin(4x)](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2%2C%5Cquad%20g%28x%29%3De%5E%7B3x%7D%2C%5Cquad%20h%28x%29%3D%5Csin%284x%29)
The derivative of a product of function is computed by deriving one function at the time, and then adding all the results:
![y' = f'(x)g(x)h(x)+f(x)g'(x)h(x)+f(x)g(x)h'(x)](https://tex.z-dn.net/?f=y%27%20%3D%20f%27%28x%29g%28x%29h%28x%29%2Bf%28x%29g%27%28x%29h%28x%29%2Bf%28x%29g%28x%29h%27%28x%29)
Let's compute the derivative of each function first:
![f'(x)=2x,\quad g'(x) = 3e^{3x},\quad h'(x)=4\cos(4x)](https://tex.z-dn.net/?f=f%27%28x%29%3D2x%2C%5Cquad%20g%27%28x%29%20%3D%203e%5E%7B3x%7D%2C%5Cquad%20h%27%28x%29%3D4%5Ccos%284x%29)
Now plug f, f', g, g', h, h' in the formula above as required:
![2xe^{3x}\sin(4x)+3x^2e^{3x}\sin(4x)+4x^2e^{3x}\cos(4x)](https://tex.z-dn.net/?f=2xe%5E%7B3x%7D%5Csin%284x%29%2B3x%5E2e%5E%7B3x%7D%5Csin%284x%29%2B4x%5E2e%5E%7B3x%7D%5Ccos%284x%29)
<span>First, calculate the difference between 15 and 12. The operation, subtraction, will give us the answer of 3. Then, divide the calculated value by 12 since this it the theoretical length of the nail. Multiply the quotient by 100% to arrive to the final answer. That is (3/12)(100%). The final answer to this item is 25% which is the last choice. </span>
Answer:
(3, 6)
Step-by-step explanation:
(x1, y1) and (x2, y2)
x2 - x1, y2 - y1
(x*, x*)
(2, 1) and (5, 7)
5 - 2, 7 - 1
(3, 6)
He cause 14 blue fish and 10 rock fish
14x8=112 10x2.5=25 112+25=137
15. The expression could be expanded to the terms below.
.87b + .87b + .87b + .87b + .87b + .87b
You could also leave each of those at (b - .13b) if they prefer. Each of them would show the cost of one discounted loaf of bread.
16. The gardener added the side lengths rather than multiplying them.