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How do you differentiate #y = 10cosx#?

Answer 1

#d/dx10cosx=-10sinx#

From the rules of differentiation, the derivative of a constant times a function is the constant times the derivative of the function. So #d/dx(10cosx) =10d/dx cosx#

Then from the rules of differentiation for trigonometric functions, the derivative of the cosine of a function is the negative sine of the function multiplied by the derivative of the function. #therefore d/dxcosx = -sinx*d/dxx#

since x can be written as #x^1#, it is a polynomial function and so its derivative is the power times the function raised to1 less than the given power, that is #d/dxx^1=1x^0=1# Hence the overall answer is #d/dx10cosx=-10sinx#

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Answer 2

Evelyn Agard

To differentiate y = 10cosx, you apply the chain rule of differentiation. The derivative of cosine function is negative sine function. So, the derivative of y = 10cosx is -10sinx. Therefore, dy/dx = -10sinx.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.