6.
Find fraction numerator d y over denominator d x end fraction
if y equals tan to the power of negative 1 end exponent left parenthesis square root of x cubed right parenthesis end root
.
7.
Find fraction numerator d y over denominator d x end fraction
if y equals tan to the power of negative 1 end exponent left parenthesis square root of x cubed right parenthesis end root
.
8.
If f left parenthesis x right parenthesis equals square root of 1 plus 8 x end root
, find f space apostrophe left parenthesis a right parenthesis
for a equals 3
and the equation of the tangent line to f left parenthesis x right parenthesis
at x equals a
.
9.
Find fraction numerator d over denominator d x end fraction open parentheses fraction numerator 1 plus sin squared x over denominator x plus tan cubed 15 x end fraction close parentheses
.
10.
The volume of a right circular cylinder of radius x
and height y
is given by v equals πx squared straight y
. Suppose that the volume of the cylinder is constant at 250 πcm cubed
. Find fraction numerator d y over denominator d x end fraction
when x equals 5
and y equals 10
.