Question

Determine f'(x) for f(x) = x22 - xy + sin x cos x - ex

Answer 1

\[f(x) = x^{22} - xy + \sin x \cos x - e^x\]
You're asked to find \(f'(x)\)?

Answer 2

Differentiate f(x) with respect to x?

Answer 3

@Error1603
how does this relate to your LAST question about slices of cake - they are in a different league in terms of level of maths....

Answer 4

So, f'(x) = 2x - y + (sin x(-sin x) + cos x ( cos x) ) - ex

Answer 5

Im stuck now

Answer 6

Welp I guess I get no help

Answer 7

So, \[f(x) = x^{22} - xy + \sin x \cos x - e^x \\ \\ f'(x)= 22x^{21}-(xy'+y)+[\sin(x)(-\sin(x))+\cos(x)\cos(x)]-e^x\]

Answer 8

\[f'(x) = 2x - y + \cos(2x) - exx ( \cos22x - \sin22x = \cos(2x) )\] Using identity. Right?

Answer 9

Using cos22x−sin22x=cos(2x))

Answer 10

Yep

Answer 11

\(\color{black}{f(x,y) = x^{22} - xy + \sin x \cos x - e^x}\) and you want to find \(\color{black}{f_x(x,y)}\)?
If this is the question, we treat \(\color{black}{y}\) like a constant (not like a function of \(\color{black}{x}\)).

\(\color{black}{f(x,y) = x^{22} - xy + \sin x \cos x - e^x}\)
\(\color{black}{f(x,y) = x^{22} - xy + \frac{1}{2}\sin (2x) - e^x}\)

I first rewrote the function, and then,
\(\color{black}{f_x(x,y) = 22x^{21} -y + \cos (2x) - e^x}\)

Answer 12

\[f(x) = x^{2} - xy + \sin x \cos x - e^x \\ \\ f'(x)= 2x-(xy'+y)+[\sin(x)(-\sin(x))+\cos(x)\cos(x)]-e^x \\ \\ f'(x)=2x-xy'-y+[\cos^2(x)-\sin^2(x)]-e^x \\ \\ f'(x)=2x-xy'-y+\cos(2x)-e^x \]

Answer 13

Thank you! I thought I would never get this.

Answer 14

If this is a partial derivative of a function wrt to \(x\).
But, if it is \(\color{black}{y = x^{22} - xy + \sin x\cos x - e^x}\), and you are looking for \(y'\),
then you solve it as follows:

\(\color{black}{y = x^{22} - xy + \sin x\cos x - e^x}\)
\(\color{black}{y = x^{22} - xy + \frac{1}{2}\sin (2x) - e^x}\)
\(\color{black}{y' = 22x^{21} - xy' + \cos (2x) - e^x}\)
\(\color{black}{y' - xy'= 22x^{21} + \cos (2x) - e^x}\)
\(\color{black}{y' (1- x)= 22x^{21} + \cos (2x) - e^x}\)

\(\color{black}{\displaystyle y' =\frac{ 22x^{21} + \cos (2x) - e^x}{1-x}}\)

Answer 15

ooooh I see

Answer 16

Thanks

Answer 17

yw