1. ## Check my answers for Higher derivatives

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

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 $y'$ should be $18(sin^22x)(cos2x)$
and
$y''=18(2cos^22xsin2x+-2sin^32x)$

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

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

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

Wolfram Mathematica Online Integrator

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

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

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