$\fraction{4 \exponential{x}{\fraction{1}{2}}}{8 \exponential{x}{\fraction{1}{3}}} $
Evaluate
\frac{\sqrt[6]{x}}{2}
Differentiate w.r.t. x
\frac{1}{12x^{\frac{5}{6}}}
গ্রাফ
শেয়ার করুন
ক্লিপবোর্ডে কপি করা হয়েছে
\frac{4^{1}\sqrt{x}}{8^{1}\sqrt[3]{x}}
Use the rules of exponents to simplify the expression.
\frac{4^{1}x^{\frac{1}{2}-\frac{1}{3}}}{8^{1}}
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\frac{4^{1}\sqrt[6]{x}}{8^{1}}
Subtract \frac{1}{3} from \frac{1}{2} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.
\frac{1}{2}\sqrt[6]{x}
Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{8}x^{\frac{1}{2}-\frac{1}{3}})
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}\sqrt[6]{x})
Do the arithmetic.
\frac{1}{6}\times \frac{1}{2}x^{\frac{1}{6}-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}.
\frac{1}{12}x^{-\frac{5}{6}}
Do the arithmetic.
উদাহরণ
দ্বিঘাত সমীকরণ
{ x } ^ { 2 } - 4 x - 5 = 0
ত্রিকোণমিতি
4 \sin \theta \cos \theta = 2 \sin \theta
রৈখিক সমীকরণ
y = 3x + 4
পাটিগণিত
699 * 533
মেট্রিক্স
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
সমকালীন সমীকরণ
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
ডিফারেন্সিয়েশন
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
ইন্টিগ্রেশন
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
লিমিট
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}