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Differentiate y = x2 + cos x - sin x.

Mathematics

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Answer

2x−sin⁡x−cos⁡x2x - \sin x - \cos x

Graph of y = x² + cos(x) − sin(x)

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Key points of y = x² + cos(x) − sin(x)
Pointxy
y-intercept01
Minimum0.70.61

Here is the differentiation for the question:

  1. y=x2+cos⁡x−sin⁡xy = x^2 + \cos x - \sin x

    Step 1: Differentiate each term using the power rule and the derivatives of cos⁡x\cos x and sin⁡x\sin x.

    dydx=ddx(x2)+ddx(cos⁡x)−ddx(sin⁡x)\frac{dy}{dx} = \frac{d}{dx}(x^2) + \frac{d}{dx}(\cos x) - \frac{d}{dx}(\sin x) dydx=2x+(−sin⁡x)−(cos⁡x)\frac{dy}{dx} = 2x + (-\sin x) - (\cos x) dydx=2x−sin⁡x−cos⁡x\frac{dy}{dx} = 2x - \sin x - \cos x

    The derivative is 2x−sin⁡x−cos⁡x2x - \sin x - \cos x.

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