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Differentiation of exponentials and logarithms

Differentiation of exponentials and logarithms

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The function f(x) = eΛ£ is identical to its derivative; use the chain rule to differentiate variables in the form eΒͺΛ£ ⁺ ᡇ. The first derivative is used to find the gradient at a given value of x.

Differentiating basic exponents

To differentiate variables in the form aΛ£, use the derivative exponent rule and the chain rule. To find the gradient of an exponential graph, use the first derivative.

Differentiating exponents

To differentiate equations and variables in the form lnx, use the following rule. To find the gradient of a natural logarithmic graph, use the first derivative.

Differentiating natural logarithm

The derivative of logarithmic functions can only be found when the base, b, is a positive real number and b β‰  1. The first derivative is used to find the gradient, m, at any point of the logarithmic curve.

Differentiating logarithms

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