What is the derivative of ${(sin x + cos x)}^{2} + {(sin x - cos x)}^{2}$ $(sinx+cosx)^2 +(sinx-cosx)^2$ ?

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What is the derivative of ${(sin x + cos x)}^{2} + {(sin x - cos x)}^{2}$ $(sinx+cosx)^2 +(sinx-cosx)^2$ ?

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Answer 1 · 2016-08-11T16:34:22

$0$ $0$

Explanation:

$f (x) = {(sin x + cos x)}^{2} + {(sin x - cos x)}^{2} = 2$ $f(x) = (sinx+cosx)^2 +(sinx-cosx)^2 = 2$ so
$\frac{d f}{d x} = 0$ $(df)/(dx) = 0$

Answer 2 · 2016-08-11T16:36:42

The function is constant so the derivative is $0$ $0$

Explanation:

${(sin x + cos x)}^{2} + {(sin x - cos x)}^{2} = ({sin}^{2} x + 2 sin x cos x + {cos}^{2} x) + ({sin}^{2} x - 2 sin x cos x + {cos}^{2} x)$ $(sinx+cosx)^2+(sinx-cosx)^2 = (sin^2x+2sinxcosx+cos^2x)+ (sin^2x-2sinxcosx+cos^2x)$

$= 1 + 2 sin x cos x + 1 - 2 sin x cos x = 2$ $= 1+2sinxcosx + 1-2sinxcosx = 2$

$\frac{d}{d x} (2) = 0$ $d/dx(2) = 0$

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What is the derivative of ${(sin x + cos x)}^{2} + {(sin x - cos x)}^{2}$ $(sinx+cosx)^2 +(sinx-cosx)^2$ ?

2 Answers

Explanation:

Explanation:

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