[latex]y=\sin(x^4)[/latex]
[latex]\implies y'=4x^3\cos(x^4)[/latex]
[latex]\implies y'=12x^2\cos(x^4)-16x^6\sin(x^4)[/latex]
At [latex]x=10[/latex], you have
[latex]y'(10)=4000\cos(10^4)[/latex]
The trick to finding out the sign of this is to figure out between which multiples of [latex]\dfrac\pi2[/latex] the value of [latex]10^4[/latex] lies.
We know that [latex]\cos x>0[/latex] whenever [latex]-\dfrac\pi2+2n\pi\cos x[/latex] for [latex]\pi\sin x[/latex] for [latex]\dfrac{5\pi}4