Use the chain rule.
Let u = 25sin²(x), such that dy/dx = dy/du · du/dx
X= mountain dew y= coke
-(5x+5y=1160)
8x+5y=1523
-5x-5y=-1160
+
8x+5y=1523
<u>3x</u>=<u>363
</u><u />3 3
x=121 g of sugar in Mt. Dew
8x+5y=1523 plug in 3 in x
24+5y-24= 1523-24
<u>5y</u>= <u>1499
</u>5 5
y= 299.8 grams of sugar in coke
Answer:
15) K'(t) = 5[5^(t)•In 5] - 2[3^(t)•In 3]
19) P'(w) = 2e^(w) - (1/5)[2^(w)•In 2]
20) Q'(w) = -6w^(-3) - (2/5)w^(-7/5) - ¼w^(-¾)
Step-by-step explanation:
We are to find the derivative of the questions pointed out.
15) K(t) = 5(5^(t)) - 2(3^(t))
Using implicit differentiation, we have;
K'(t) = 5[5^(t)•In 5] - 2[3^(t)•In 3]
19) P(w) = 2e^(w) - (2^(w))/5
P'(w) = 2e^(w) - (1/5)[2^(w)•In 2]
20) Q(W) = 3w^(-2) + w^(-2/5) - w^(¼)
Q'(w) = -6w^(-2 - 1) + (-2/5)w^(-2/5 - 1) - ¼w^(¼ - 1)
Q'(w) = -6w^(-3) - (2/5)w^(-7/5) - ¼w^(-¾)
Here is your answer is slope-intercept form: y=-2x-15
