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Find the derivative of the following function8xy =In 4xy'=

Question
Find the derivative of the following function
8x
y =
In 4x
y'=
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Find the derivative of the following function 8x y = In 4x y'=

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check_circleAnswer
Step 1

Since the given function is a ratio of two differentiable functions, we use the quotient rule.

If f(x) 1then
h(x)
f(x)= x)g '(x)-h'(x)g(x)
hx)]
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If f(x) 1then h(x) f(x)= x)g '(x)-h'(x)g(x) hx)]

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Step 2

Differentiating the given function on both sides with respect to x as per step 1;

8x
dy
dx dxn 4x
In 4x d(e8)
dy
d(In 4x)
8x
dx
dx
dx
(In 4x)
1
..4
4x
In 4x 8e
dy
(In 4x)2
dx
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8x dy dx dxn 4x In 4x d(e8) dy d(In 4x) 8x dx dx dx (In 4x) 1 ..4 4x In 4x 8e dy (In 4x)2 dx

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Step 3

Simplify and take out...

1
In 4x 8ee"
dy
х
(In 4x)2
dx
n 4x- 8
dy
х
8x
(In 4x)2
dx
dy
1
8x
е
dx
(n 4x)
In 4x
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1 In 4x 8ee" dy х (In 4x)2 dx n 4x- 8 dy х 8x (In 4x)2 dx dy 1 8x е dx (n 4x) In 4x

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Tagged in

Math

Calculus

Derivative

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