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
Answer:
y=35
Step-by-step explanation:
y in (-oo:+oo)
14 = (2*y)/5 // - (2*y)/5
14-((2*y)/5) = 0
(-2/5)*y+14 = 0
14-2/5*y = 0 // - 14
-2/5*y = -14 // : -2/5
y = -14/(-2/5)
y = 35
y = 35
a/b * b/c * c/d * d/e is equal to a/e provided that b, c, d,
and e are not zero
PROVE
a/b * b/c * c/d * d/e
= (a/b *b/c) * (c/d * d/e)
= ab/bc * (c/d * d/e)
= a/c * (c/d * d/e)
= a/c * (cd/de)
= a/c * c/e
= ac/ce
= a/e
Therefore, a/b * b/c * c/d * d/e is equal to a/e provided that
b, c, d, and e are not zero
Answer:
7
Step-by-step explanation:
Step-by-step explanation:
<h2><u>☼︎</u><u>Given :</u></h2>
- The floor of a drawing room consist of 2000 tiles .Each tiles is rectangular in shape , of dimensions ,30 cm × 20 cm.
<h2><u>☼︎</u><u>To Find :</u></h2>
<h2><u>☼︎</u><u>Solution :</u></h2>
<u>~ Formula </u><u>U</u><u>s</u><u>e</u><u>d</u><u>:</u>
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
<u>~ Calculating the</u><u> Area of Tiles </u>
<u>~ Calculating Area of the </u><u>Drawing Room :</u>
<u>~ Therefore :</u>
❝ Area of the Drawing room is 1200000 cm² or 12000 m² . ❞