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
Here is the set using D = rt.
Jet 1:
rate = 377 mph
time = x
Distance = 9128 miles
Jet 2:
rate = 275 mph
time = x
Distance = 9128 miles
Equation:
377x + 275x = 9128
You finish.
Answer:
373737373746372838484883848r
Answer:
the lease common multiple is 8
Answer:
A. -18·10^6
Step-by-step explanation:
The rules of exponents apply to powers of 10 used in scientific notation. The associative and commutative properties of multiplication also apply.
<h3>Application</h3>
(a^b)(a^c) = a^(b+c)
The numerical product is ...
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<em>Additional comment</em>
Expressed in scientific notation, the result would be ...
Your calculator can perform this multiplication for you.
