Differentiate w.r.t. x
48x^{3}+3
Evaluate
12x^{4}+3x-1
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4\times 12x^{4-1}+3x^{1-1}
The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.
48x^{4-1}+3x^{1-1}
Multiply 4 times 12.
48x^{3}+3x^{1-1}
Subtract 1 from 4.
48x^{3}+3x^{0}
Subtract 1 from 1.
48x^{3}+3\times 1
For any term t except 0, t^{0}=1.
48x^{3}+3
For any term t, t\times 1=t and 1t=t.
Examples
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Limits
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