1. ## Check my answers for Higher derivatives

1) find y' if $\displaystyle y=2sin2x+5cos3x-4$
Attempt:
$\displaystyle (2)sin(2x)+(5)cos(3x-4)$
$\displaystyle =4cos2x-15sin3x-4$
2) find y" if $\displaystyle y=cotx$
Attempt:
y'=$\displaystyle -csc^2x$
y"=$\displaystyle 2csc^2xcotx$
3) find y" if $\displaystyle y=x.tanx$
Attempt:
y'=$\displaystyle (x)(sex^2x)+tanx$
y"=$\displaystyle (x)(-2sec^2x)tanx+sec^4x$
4)find y" if $\displaystyle 3sin^3(2x)$
Attempt;
y'=$\displaystyle 18(sin^2x)(cos2x)$
y"=$\displaystyle -36 sin^3 2x+4cos^2 2x sin2x$
5)find y" if $\displaystyle x^5+3x^3+6$
Attempt:
y'=$\displaystyle 5x^4+9x^2$
y"=$\displaystyle 20x^3+18x$

Please check is my answer are correct,if not write the correct solution in steps...
Thank you

2. You should use this site to check your derivatives

Wolfram Mathematica Online Integrator

For no.4 $\displaystyle y'$ should be $\displaystyle 18(sin^22x)(cos2x)$
and
$\displaystyle y''=18(2cos^22xsin2x+-2sin^32x)$

No.3
$\displaystyle y'=(x)(sex^2x)+tanx$
$\displaystyle y''=2xsec^3xsinx+2sec^2x$

N.B
$\displaystyle \frac{d}{dx}(xsec^2x)=2xsec^3xsinx+sec^2x$

3. Originally Posted by I-Think
You should use this site to check your derivatives

Wolfram Mathematica Online Integrator

For no.4 $\displaystyle y'$ should be $\displaystyle 18(sin^22x)(cos2x)$
and
$\displaystyle y''=18(2cos^22xsin2x+-2sin^32x)$

No.3
$\displaystyle y'=(x)(sex^2x)+tanx$
$\displaystyle y''=2xsec^3xsinx+2sec^2x$

N.B
$\displaystyle \frac{d}{dx}(xsec^2x)=2xsec^3xsinx+sec^2x$
So are there any mistakes ,btw thnx for the site but i am differentiating not integrating