Logarithmic differentiation means tAke logarithm of both sides to make the function easier to find the derivative.

y = (sinx)^lnx

ln(y) = ln((sinx)^lnx)

power rule logarithm

ln(y) = ln(x) ln(sinx)

Take derivative

y'/y = ln(sinx)(1/x) + ln(x) cosx/sinx

multiply both sides by y

y' = y( ln(sinx)/x + ln(x)cotx )

remember y = (sinx)^lnx
sub this in for y

y' = (ln(sinx)/x + ln(x)cotx)(sinx)^lnx

4 0

3 years ago

PLEASE HELP!!!!!!!!! ASAP!!!!! I REWARD BRAINLIEST!!!! HAVE CLASS IN 30 MINUTES!1111

KiRa [710]

Answer:

$y = \dfrac{1}{3}x + 1$

Step-by-step explanation:

The given line is in slope-intercept form,

y = mx + b,

where m is the slope.

The slope of the given line is 1/3, so m = 1/3.

Parallel lines have equal slopes, so the slope of the parallel line is also 1/3.

y = 1/3 x + b

Now we can find the equation of the parallel line through point (6, 3) by using the given point's coordinates for x and y and solving for b.

3 = (1/3)(6) + b

3 = 2 + b

b = 1

Equation: $y = \dfrac{1}{3}x + 1$

8 0

2 years ago

Read 2 more answers

if one store has 360 items and another store has 100 of the same items, express the ratio of the items

choli [55]

360:100 or 360 to 100

4 0

3 years ago

- A contractor plans to build a rectangular office complex. The floor area on the first floor of the

Neko [114]

Answer:

Width = 30

Step-by-step explanation:

Area = 18x * 10y = 180xy

Length = 6xy

Width = ?

Since the shape of the office complex is a rectangle,

Area of a rectangle = length × width

180xy = 6xy × width

Width = 180xy / 6xy

Width = 30

4 0

3 years ago