Question

please solve it as fast as you can ​

Answer 1

Explanation:

1. d/dx ( 3x^5 + sin 2x )

= d/dx ( 3x^5 ) + d/dx ( sin 2x )

= 15 x^4 + 2 cos 2x

$d \div dx \: ( \: x ^{n} ) \: = n \: x ^{n - 1}$

2. d/dx ( x^7/2 - 1/7x^4 )

= d/dx( x^7/2 ) - d/dx( 1/7x^4 )

= 7/2 x^5/2 + 4/7 x^-5

3. d/ dx ( 3 cos 7x + 4x^1/2 )

= d/ dx ( 3 cos 7x ) + d/ dx ( 4x^1/2 )

= -21 sin 7x + 2/ x^1/2

4. d/dx ( x^1/2 + 1/ x^1/2 )

= d/dx ( x^1/2 ) + d/dx ( 1/ x^1/2 )

= 1/2(x^1/2) - 1/ 2 ( x^3/2 )