Evaluate
\frac{8\sqrt{2}}{5x+3}
Differentiate w.r.t. x
-\frac{40\sqrt{2}}{\left(5x+3\right)^{2}}
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\frac{\sqrt{5^{3}+3}}{3+5x}
To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.
\frac{\sqrt{125+3}}{3+5x}
Calculate 5 to the power of 3 and get 125.
\frac{\sqrt{128}}{3+5x}
Add 125 and 3 to get 128.
\frac{8\sqrt{2}}{3+5x}
Factor 128=8^{2}\times 2. Rewrite the square root of the product \sqrt{8^{2}\times 2} as the product of square roots \sqrt{8^{2}}\sqrt{2}. Take the square root of 8^{2}.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\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]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}