Solutions-derivatives-Exponential sadhas odsakjhd kjsad PDF

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Section 4.8 The derivative of the exponential and natural logarithm functions Practice Problems

2. (a) 3e3x

(b)

–e–x

(c)

1/x

(d)

3. (a) For the product rule we put u = x4

and

v = ln x

for which du  4x 3 dx

and

dv 1  dx x

By the product rule

dy 1 x 4   ln x 4x 3 x dx  x3  4 x3 ln x  x3 (1  4 ln x) (b) By the chain rule 2 2 dy e x 2x  2xe x dx

(c) If u ln x

and

du 1  and dx x

dv 1 dx

v x  2

then

By the quotient rule

1 (x  2)  ( ln x )1 dy x  dx (x  2)2 x 2  x ln x (multiply top and bottom by x ) x( x  2)2

1/x...