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The
derivative of a power is the exponent times x to the power of the exponnent
minus one.
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The
derivative of a sum is the sum of the derivatives of each function being
added.
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The
derivative of a difference is the difference of the derivatives of the functions
being subtracted.
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The
derivative of a constant times a function is the constant times the derivative
of the function.
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The
derivative of a constant is zero.
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The
derivative of a product is the derivative of the first factor multiplied
by the second factor plus the first factor multiplied by the derivative
of the second factor.
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The
derivative of a quotient is the quotient of the derivative of the numerator
multiplied by the denominator minus the numerator multiplied by the derivative
of the denominator to the square of the denominator.
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The
derivative of an exponential function is the product of the exponential
function and the natural logarithm of the base.
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Since
the natural logarithm of e is 1, the derivative of e^(x) is e^(x).
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The
derivative of a logarithm is 1 divided by the product of the natural logarithm
of the base and x.
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The
derivative of the natural logarithm of x is 1/x.
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The
derivative of the sine of x is the cosine of x.
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The
derivative of the cosine of x is the opposite of the sine of x.
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The
derivative of the tangent of x is the square of the secant of x.
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The
derivative of the secant of x is the product of the secant of x and the
tangent of x.
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The
derivative of the cosecant of x is the opposite of the product of the cosecant
of x and the cotangent of x.
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The
derivative of the cotangent of x is the opposite of the square of the cosecant
of x.
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