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5-52.

Differentiate if possible. If the function is one we have not yet studied, say so and explain how you know. Be sure to use the appropriate notation.

Hint:

You have the skills to find the derivative of five out of six of the problems below.

$y = x^{100} + 100x$
Hint (a):
Power Rule.

$H ( t ) = t ^ { - 4 } - 6 \sqrt { t }$
Hint (b):
Before differentiating, rewrite the square root with a fractional exponent.

$y = x · 2^x$
Hint (c):
Do you know how to find a derivative of $2^x$ ?

$y = x^8\operatorname{ cos }x$
Hint (d):

$f(x) = x^5 (x^3 + π)$
Hint (e):
Distribute first. Or use the Product Rule.

$y = \frac { 7 } { x } - \frac { x } { 7 }$
Hint (f):
Before differentiating, rewrite the first fraction with exponents.

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