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How do you find the derivative of #3x² + 2sin(x - 5)#?

Answer 1

Isaiah Allen

#6x+2cos(x-5)#

By using normal rules of differentiation we get

#d/dx[3x^2+2sin(x-5)]=6x+2cos(x-5)#

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Answer 2

Christopher Agresta

To find the derivative of (3x^2 + 2\sin(x - 5)), you can apply the rules of differentiation. The derivative of (3x^2) with respect to (x) is (6x), and the derivative of (\sin(x - 5)) is (\cos(x - 5)). Using the chain rule for the sine function, the derivative of (\sin(x - 5)) with respect to (x) is (\cos(x - 5)) multiplied by the derivative of (x - 5), which is simply 1. Therefore, the derivative of (2\sin(x - 5)) is (2\cos(x - 5)). So, the derivative of (3x^2 + 2\sin(x - 5)) with respect to (x) is (6x + 2\cos(x - 5)).

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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.