Q&A for How to Take Derivatives

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What is the derivative of x^0.09?

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By the power rule, you would first multiply the whole equation by the exponent, which is 0.09 so you get 0.09x^0.09. Then, you subtract the power by one, so it becomes 0.09x^(-.91).

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What is the second derivative of 1/x?

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2 x^-3

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What is the derivative of a logarithmic function?

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The derivative of a log function is the derivative of the function divided by the function itself. For example, the derivative of log(x) would be the derivative of x is 1 divided by x, and so log(x) = 1/x.

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What is the derivative of X power of infinite X?

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It is infinity.

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Isn't 1/x for positive x the derivative of ln(x)? Wouldn't the derivative of log(x) be 1/(x*ln(10)) for x>0?

Mark LS5703724

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Yes , it is. The base of log(x) is log base 10, 2nd, the formula is d/dx(log_a(X) = 1/xln(a) and after substituting the value of a into the equation, we will get 1/x(ln(a)).

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How can I understand any of this?

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See Understand Calculus and related articles.

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What is the derivative of 1/x?

I_l1ke_gam3s

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d/dx(1/x) = d/dx(x^-1) = -x^-2 = -1/x^2

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