CPM Homework Help : CALC3RD Problem 8-6

CPM Homework Banner

Home > CALC3RD > Chapter Ch8 > Lesson 8.1.1 > Problem 8-6

8-6.

Compute the following derivatives.

$\frac { d } { d x } \sqrt [ 3 ] { 5 x ^ { 2 } - 17 x }$
Hint (a):
Before differentiating, rewrite the expression with an exponent.
Hint (a):
Take the derivative using the Chain Rule.

$\frac { d } { d x } ( ( 4 x ^ { 3 } + 2 x - 5 ) ( 8 - 7 x ^ { 3 } ) )$
Hint (b):
You can expand the polynomial expression before differentiating or you can compute the derivative using the Product Rule.

$\frac { d } { d x } \operatorname { sin } ( \operatorname { sin } ( t ) )$
Hint (c):
Chain Rule

$\frac { d } { d x } \int _ { 7 x } ^ { \operatorname { cos } ( x ) } \operatorname { ln } ( t ^ { 2 } ) d t$
Hint (d):
$≠ \ln(\cos^2(x)) - \ln(49x^2)$
Hint (d):
The Fundamental Theorem of Calculus, part 1 states that the derivative of an INDEFINITE integral is the original function. But this is a DEFINITE integral.
Answer (d):
$= −\sin(x)\ln(\cos^2(x)) − 7\ln(49x^2)$

© 2022 CPM Educational Program. All rights reserved.