Using Identities to simplify expression

Question

I have the following expression which is supposed to be solved by chain rule to find dw/dt

$w$ = $5 \cos(xy)$ $-$ $\sin(xz)$ where $x = 1/t$ , $y=t$ , $z=t^3$

My final answer is ( added wolfram results just to be sure. They are the same as mine)

Results

And following is the answer that I want to get.

Result = $-2t \cos t^2$

I am trying to solve it through different Identities but of no luck

NOTE: This is actualy a question from Calculus (10 Edition) by Howard Anton Exercise 13.5 Q9

Answer 1

Hint: Use direct substitution for $t$ in $x$, $y$ and $z$. One of the first terms will be a constant once the values of $t$ are substituted in.

ANSWER:

For $$w = 5 \cos(xy) - \sin(xz)$$ where $$x=1/t, y=t, z=t^3$$

let's simplify in terms of $t$. $xy$ in this case is $\frac {1}{t} \times t$ or $1$. $xz$ is $\frac {1}{t} \times t^3$ or $t^2$. Thus we have $$w = 5 \cos 1 - \sin t^2$$

Taking the derivative of $w$ with respect to $t$ is easy. $5 \cos 1$ is a constant, so that derivative will be $0$. Taking the derivative of $-\sin t^2$ by using the chain rule leaves us with $$-2t \cos t^2$$

Answer 2

There is no way for such a reduction to work: evaluate the two expressions at an easy-to-calculate point (e.g. $t=1/\pi$). The values are numerically different, so the two expressions are not equal. Are you sure you have copied the statement of the problem accurately?