❥Find the derivative of sinx.
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Answer:
Cos x
Step-by-step explanation:
The derivative of sin x
d/dx sin x = cos x
To prove that, we will apply the definition of the derivative. First, we will calculate the difference quotient.
Derivative of sin x = Derivative of sin x , Problem 1,
= Derivative of sin x , on dividing numerator
and denominator by 2,
= Derivative of sin x
We will now take the limit as h Right arrow0. But the limit of a product is equal to the product of the limits. (Lesson 2.) And the factor on the right has the form sin θ/θ. Therefore, according to the Lemma, as h Right arrow0 its limit is 1. Therefore,
d
dx sin x = cos x.
We have established the formula.
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- Find the Derivative of sinx . ?
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Hence, the Derivate of sin(x) is cos(x).
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