Differentiate the following?

Question

cos(1+e^x)

Answer 1

d/dx cos(1+e^x)

= - sin(1 + e^x) * d/dx (1 + e^x)

= - e^x sin(1 + e^x).

Answer 2

-(e^x)sin(1+e^x)

Answer 3

y=cos(u)

dy/du=-sinu

u=1+e^x

du/dx=0+e^x

dy/dx=-e^xsinu

=-e^xsin(1+e^x)

Answer 4

[cos(1+e^x)]' = -sin(1+e^x) * [(1+e^x)']

                    = -sin(1+e^x) * (0+e^x)

                    = -e^x * sin(1+e^x)

Answer 5

let y =cos(1+e^x)

y' = -e^x * sin (1 + e^x)

=)

Answer 6

Differentiate this though the use of the chain rule. This yields the answer;

e^x [-sin(1+e^x)]

For a more extended solution (showing the chain rule in full);

Let

            u=1+e^x  

and

            y=cos(1+e^x)-------->y=cos(u)

Therefore;

du/dx=e^x

dy/du=-sin(u)

dy/dx=dy/du * du/dx

        =e^x * [-sin(u)]

        = -e^x*sin(u)

        = -e^x * sin(1+e^x)

Keep practicing your chain rule, and you should be able to solve this by inspection very efficiently (try to notice the general way to solve the equation, by recognising which part is the 'u'; being able to solve by noticing general trends becomes extremely handy in integration)

Answer 7

i'd rather not