Are these the correct expressions for ## dF/dy' ##?

[Math100]

Homework Statement

Find the expressions for $dF/dy'$ when
a) $F(y')=(1+y'^2)^{\frac{1}{4}}$
b) $F(y')=sin (y')$
c) $F(y')=exp(y')$

Relevant Equations

None.

a) $dF/dy'=\frac{1}{4}(1+y'^2)^{\frac{-3}{4}}\cdot 2y'$
b) $dF/dy'=cos (y')$

I just took the derivatives above and found out these expressions, but may anyone please check/verify to see if these expressions for $dF/dy'$ are correct? Also, I do not understand part c). What does 'exp' indicate in here?

 

[fresh_42]

Homework Statement: Find the expressions for $dF/dy'$ when
a) $F(y')=(1+y'^2)^{\frac{1}{4}}$
b) $F(y')=sin (y')$
c) $F(y')=exp(y')$
Relevant Equations: None.

a) $dF/dy'=\frac{1}{4}(1+y'^2)^{\frac{-3}{4}}\cdot 2y'$
b) $dF/dy'=cos (y')$

I just took the derivatives above and found out these expressions, but may anyone please check/verify to see if these expressions for $dF/dy'$ are correct? Also, I do not understand part c). What does 'exp' indicate in here?

$\exp(y')$ means $e^{y'}.$

What you wrote is correct, but why is there a prime at the $y$'s? The same could be written with just $y$ or $t$ as the variable name. $y'$ normally indicates a derivative.

 

[Math100]

$\exp(y')$ means $e^{y'}.$

What you wrote is correct, but why is there a prime at the $y$'s? The same could be written with just $y$ or $t$ as the variable name. $y'$ normally indicates a derivative.

I don't know either. So what should the book normally express these primes then, instead? Also, if $exp(y')$ mean $e^{y'}$. Then the expression for $dF/dy'$ is $dF/dy'=e^{y'}$?

 

[fresh_42]

I don't know either. So what should the book normally express these primes then, instead? Also, if $exp(y')$ mean $e^{y'}$. Then the expression for $dF/dy'$ is $dF/dy'=e^{y'}$?

Yes.

 

[Math100]

Yes.

Thank you so much for verifying!