Calculating derivatives Find dy&gt;dx for the following functions. y=sin⁡x+cos⁡x

Step 1 Derivative of sin⁡x is: ddxsin⁡x=cos⁡x Derivative of cos⁡x is: ddxcos⁡x=−sin⁡x Step 2 The given function is: y=sin⁡x+cos⁡x We have to find the derivative of the given function and we need to find the value of dydx. Differentiate the given function with respect to x. dydx=ddx(sin⁡x+cos⁡x) dydx=ddx(sin⁡x)+ddx(cos⁡x) dydx=cos⁡x−sin⁡x Step 3 Answer: The derivative of the given function is dydx=cos⁡x−sin⁡x.

Explained: "Calculating derivatives Find dy>dx for the following functions...."

College
Calculus and Analysis
Differential Calculus
Derivatives

Chesley

Answered question

2021-10-17

Calculating derivatives Find dy>dx for the following functions.

y = \sin x + \cos x

Answer & Explanation

opsadnojD

Skilled2021-10-18Added 95 answers

Step 1
Derivative of

\sin x

is:

\frac{d}{d x} \sin x = \cos x

Derivative of

\cos x

is:

\frac{d}{d x} \cos x = - \sin x

Step 2
The given function is:

y = \sin x + \cos x

We have to find the derivative of the given function and we need to find the value of

\frac{d y}{d x}

.
Differentiate the given function with respect to x.

\frac{d y}{d x} = \frac{d}{d x} (\sin x + \cos x)

\frac{d y}{d x} = \frac{d}{d x} (\sin x) + \frac{d}{d x} (\cos x)

\frac{d y}{d x} = \cos x - \sin x

Step 3
Answer: The derivative of the given function is

\frac{d y}{d x} = \cos x - \sin x

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