Answer: 15e^5x
Step - by - step
y=3e^5x - 2
By the sum rule, the derivative of 3e^5x - 2 with respect to x is d/dx [ 3e^5x ] + d/dx [-2].
d/dx [ 3e^5x ] + d/dx [ -2 ]
Evalute d/dx [ 3e^5x ]
Since 3 is constant with respect to x , the derivative of 3e^5x with respect to x is
3 d/dx [ e^5x ].
3 d/dx [ e^5x ] + d/dx [ -2 ]
Differentiate using the chain rule, which states that d/dx [ f(g(x))] is f' (g(x)) g' (x) where f(x) = e^x and g(x) = 5x.
To apply the Chain Rule, set u as 5x.
3 ( d/du [ e^u] d/dx [5x] ) + d/dx [ -2]
Differentiate using the Exponential rule which states that d/du [ a^u ] is a^u ln(a) where a=e.
3( e^u d/dx[5x] ) + d/dx [ -2 ]
Replace
3(e^5x d/dx [5x] ) + d/dx [ -2 ]
3(e^5x( 5 d/dx [x] )) + d/dx [ -2 ]
Diffentiate using the Power Rule which states that d/dx [x^n] is nx^n-1 where n=1.
3(e^5x(5*1)) + d/dx [-2]
3 ( e^5x * 5 ) + d/dx [-2]
Multiply 5 by 3
15e^5x + d/dx [-2]
Since -2 is constant with respect to x, the derivative of -2 with respect to x is 0.
15e^5x + 0
15e^5x
<span>A = 4.7 + C
where A represents the students who got A's, and C is the number of hours that the C-grade students spent on homework per week</span>
X=5, y=-4
(5,-4)
do you need the work?
If there are 4 pens there will be 1 pencil, if there is 1 pencil there will be 4 pens
If the ratio is factored to a number, let's say 3, then there will be 12 pens for every 3 pencils
Hello there!
Okay, I don't know if this is a "select all that apply", but I believe that answers 1, 2, and 3 are all equivalent to 0.53.
To see how these fractions are equal, I divided the numerators by the denominators. For instance, you could have 4 over 5 (4/5) and divide 4 by 5 (4/5) to get 0.8. Now you'll do the same thing for the fractions given
24/45=0.533...
8/15=0.533...
48/90=0.533...
5/9=0.5556
As you can see, the only fraction that doesn't equal 0.53, or the outlier, is 5/9 or 0.5556
I hope this helps you out!
