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(d)/(dx)(x^((3)/(4)))=

$\frac{d}{d x}\left(x^{\frac{3}{4}}\right)=$

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Csc, sec, and cot of special angles

Full solution

Q.

\frac{d}{d x}\left(x^{\frac{3}{4}}\right)=

Apply Power Rule: To find the derivative of $x^{(3/4)}$ with respect to $x$ , we will use the power rule for differentiation. The power rule states that if $f(x) = x^n$ , then $f'(x) = n \cdot x^{(n-1)}$ .
Differentiate $x^{\frac{3}{4}}$ : Applying the power rule to $x^{\frac{3}{4}}$ , we differentiate as follows: $\newline$ $\frac{d}{dx}(x^{\frac{3}{4}}) = \frac{3}{4}\cdot x^{(\frac{3}{4}-1)}$
Subtract Exponent: Subtract $1$ from the exponent $(3/4)$ to get the new exponent: $\newline$ $(3/4) - 1 = (3/4) - (4/4) = -1/4$
Write New Derivative: Now, write the derivative with the new exponent: $\frac{d}{dx}(x^{\frac{3}{4}}) = \frac{3}{4}\cdot x^{-\frac{1}{4}}$
Final Answer: The derivative of $x^{(3/4)}$ with respect to $x$ is $(3/4)\cdot x^{(-1/4)}$ . This is the final answer in simplified form.

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