Here, we show you a step-by-step solved example of calculus. This solution was automatically generated by our smart calculator:
Apply the quotient rule for differentiation, which states that if $f(x)$ and $g(x)$ are functions and $h(x)$ is the function defined by ${\displaystyle h(x) = \frac{f(x)}{g(x)}}$, where ${g(x) \neq 0}$, then ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$
The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$
The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$
The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if ${f(x) = \sin(x)}$, then ${f'(x) = \cos(x)\cdot D_x(x)}$
Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number
Multiplying fractions $\frac{1}{2} \times \frac{1}{x^{\left|-\frac{1}{2}\right|}}$
Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number
Multiplying fractions $\frac{1}{2} \times \frac{1}{\sqrt{x}}$
Multiply $1$ times $1$
Multiplying fractions $\frac{1}{2} \times \frac{1}{\sqrt{x}}$
Multiply the fraction by the term
Any expression multiplied by $1$ is equal to itself
Multiply the fraction by the term
Combine all terms into a single fraction with $2\sqrt{x}$ as common denominator
Multiply $-1$ times $2$
When multiplying two powers that have the same base ($\sqrt{x}$), you can add the exponents
Cancel exponents $\frac{1}{2}$ and $2$
Divide fractions $\frac{\frac{\sin\left(x\right)-2x\cos\left(x\right)}{2\sqrt{x}}}{\sin\left(x\right)^2}$ with Keep, Change, Flip: $\frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}$
Combine all terms into a single fraction with $2\sqrt{x}$ as common denominator
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