### Home > APCALC > Chapter 8 > Lesson 8.1.1 > Problem8-6

8-6.

Compute the following derivatives. Homework Help ✎

1. $\frac { d } { d x } \sqrt [ 3 ] { 5 x ^ { 2 } - 17 x }$

Before differentiating, rewrite the expression with an exponent.

Take the derivative using the Chain Rule.

1. $\frac { d } { d x } ( ( 4 x ^ { 3 } + 2 x - 5 ) ( 8 - 7 x ^ { 3 } ) )$

You can expand the polynomial expression before differentiating or you can compute the derivative using the Product Rule.

1. $\frac { d } { d x } \operatorname { sin } ( \operatorname { sin } ( t ) )$

Chain Rule

1. $\frac { d } { d x } \int _ { 7 x } ^ { \operatorname { cos } ( x ) } \operatorname { ln } ( t ^ { 2 } ) d t$

$≠ \ln(\cos^2(x)) - \ln(49x^2)$

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.

$= −\sin(x)\ln(\cos^2(x)) − 7\ln(49x^2)$