# Problem 1

Compute the derivative of the following functions directly from the definition

*f*(*x*) =*x*^{3}.*f*(*x*) =^{p}(*x*).*f*(*x*) =*x*.*f*(*x*) =*c*with some constant*c*.

# Problem 2

Compute the derivatives of the following functions

- where
*b*is a constant *g*(*t*) = cos(*ωt*+*φ*) + sin(*ωt*+*φ*) where*ω*and*φ*are constants*h*(*s*) = cos(*s*^{2 }+*s*) + sin(*s/*2)*j*(*x*) = ln(*x*^{a}^{2 }+*x*^{−a}^{2}) where*a*is a constant

*Note: *You can use (ln*x*)^{0 }= 1*/x *from the lecture

- e)
*k*(*x*) = ln(*x*+^{a }*b*) where^{x}*a*and*b*are constants *l*(*x*) =*x*^{2 }exp(−*x*^{2})*m*(*x*) =*x*^{x}^{2 }

*Note for e) and g): *You cannot directly work with something of the form *a ^{x }*(with some

*a*) but only with something of the form

*e*(with some

^{cx }*c*). Transform the function accordingly before differentiation.

Jacobs University of Bremen

# Problem 3

Use the definition of the derivative, , to show that the function *f*(*x*) = |*x*| is not differentiable at *x *= 0.

## Reviews

There are no reviews yet.