Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter5: Graphs And The Derivative
Section5.CR: Chapter 5 Review
Problem 13CR
Related questions
Question
please solve 342
![For the following exercises, find f'(x) for each function.
331. f(x) = x² ex
332. f(x)=x
e
333. f(x) = ex³lnx
334. f(x) = √e²x + 2x
2x
335. f(x)= =
10%
In 10
337. f(x) = 24x + 4x²
338. f(x) = 3 sin 3x
339. f(x)= xx
340. f(x) = ln(4x³ + x)
341. f(x) = In√5x - 7
342. f(x)=x²ln 9x
343. f(x) = log (secx)
336. f(x) =
+3) ³
344. f(x) = log7(6x4 +
Inx
350. y=(x²-1) ¹x
cotx
351. y=xCo
Page
352. y =
1
x+11
√√²-4
353. y=x-1/2 (x²+3) ²/3 (3x-4)4
354. [T] Find an equation of the tangent line to the graph
(x²-1)
of f(x) = 4xe
both the function and the tangent line.
of 4
at the point where x = −1. Graph
355. [T] Find the equation of the line that is normal to the
graph of f(x) = x 5* at the point where x = 1. Graph
both the function and the normal line.
356. [T] Find the equation of the tangent line to the graph
of x³ - xlny + y² = 2x+5 at the point where x = 2.
(Hint: Use implicit differentiation to find
the curve and the tangent line.
357. Consider the function y = x²
x l/x
dy
dx
.) Graph both
for x > 0.
a. Determine the points on the graph where the
tangent line is horizontal.
b. Determine the points on the graph where y'>0
and those where y' < 0.
ZOOM
+
|](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03fd5f25-eded-4046-9c65-9e89b5e28b89%2F6c96d8fd-26b4-45c8-bd35-fbd69c1c125a%2Fwxzr43_processed.png&w=3840&q=75)
Transcribed Image Text:For the following exercises, find f'(x) for each function.
331. f(x) = x² ex
332. f(x)=x
e
333. f(x) = ex³lnx
334. f(x) = √e²x + 2x
2x
335. f(x)= =
10%
In 10
337. f(x) = 24x + 4x²
338. f(x) = 3 sin 3x
339. f(x)= xx
340. f(x) = ln(4x³ + x)
341. f(x) = In√5x - 7
342. f(x)=x²ln 9x
343. f(x) = log (secx)
336. f(x) =
+3) ³
344. f(x) = log7(6x4 +
Inx
350. y=(x²-1) ¹x
cotx
351. y=xCo
Page
352. y =
1
x+11
√√²-4
353. y=x-1/2 (x²+3) ²/3 (3x-4)4
354. [T] Find an equation of the tangent line to the graph
(x²-1)
of f(x) = 4xe
both the function and the tangent line.
of 4
at the point where x = −1. Graph
355. [T] Find the equation of the line that is normal to the
graph of f(x) = x 5* at the point where x = 1. Graph
both the function and the normal line.
356. [T] Find the equation of the tangent line to the graph
of x³ - xlny + y² = 2x+5 at the point where x = 2.
(Hint: Use implicit differentiation to find
the curve and the tangent line.
357. Consider the function y = x²
x l/x
dy
dx
.) Graph both
for x > 0.
a. Determine the points on the graph where the
tangent line is horizontal.
b. Determine the points on the graph where y'>0
and those where y' < 0.
ZOOM
+
|
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