What is the derivative of (i+xj+2xk/(sqrt(5x^2+1))) ?

The derivative of (i+xj+2xk/(sqrt(5x^2+1))) is (j+2k)/((1+5x^2)^{3/2)}-i(5x)/((1+5x^2)^{3/2)}

What is the first derivative of (i+xj+2xk/(sqrt(5x^2+1))) ?

The first derivative of (i+xj+2xk/(sqrt(5x^2+1))) is (j+2k)/((1+5x^2)^{3/2)}-i(5x)/((1+5x^2)^{3/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{i + x j + 2 x k}{5 x ^{2} + 1})

\frac{j + 2 k}{( 1 + 5 x ^{2} ) ^{\frac{3}{2}}} - i \frac{5 x}{( 1 + 5 x ^{2} ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{i + x j + 2 x k}{5 x ^{2} + 1})

Simplify

\frac{i + x j + 2 x k}{5 x ^{2} + 1} : \frac{( j x + 2 k x ) 1 + 5 x ^{2}}{1 + 5 x ^{2}} + i \frac{1 + 5 x ^{2}}{1 + 5 x ^{2}}

= \frac{d}{d x} (\frac{( j x + 2 k x ) 1 + 5 x ^{2}}{1 + 5 x ^{2}} + i \frac{1 + 5 x ^{2}}{1 + 5 x ^{2}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{( j x + 2 k x ) 1 + 5 x ^{2}}{1 + 5 x ^{2}}) + \frac{d}{d x} (i \frac{1 + 5 x ^{2}}{1 + 5 x ^{2}})

\frac{d}{d x} (\frac{( j x + 2 k x ) 1 + 5 x ^{2}}{1 + 5 x ^{2}}) = \frac{j + 2 k}{( 1 + 5 x ^{2} ) ^{\frac{3}{2}}}

\frac{d}{d x} (i \frac{1 + 5 x ^{2}}{1 + 5 x ^{2}}) = - \frac{5 i x}{( 1 + 5 x ^{2} ) ^{\frac{3}{2}}}

= \frac{j + 2 k}{( 1 + 5 x ^{2} ) ^{\frac{3}{2}}} - \frac{5 i x}{( 1 + 5 x ^{2} ) ^{\frac{3}{2}}}

Simplify

\frac{j + 2 k}{( 1 + 5 x ^{2} ) ^{\frac{3}{2}}} - \frac{5 i x}{( 1 + 5 x ^{2} ) ^{\frac{3}{2}}} : \frac{j + 2 k}{( 1 + 5 x ^{2} ) ^{\frac{3}{2}}} - i \frac{5 x}{( 1 + 5 x ^{2} ) ^{\frac{3}{2}}}

= \frac{j + 2 k}{( 1 + 5 x ^{2} ) ^{\frac{3}{2}}} - i \frac{5 x}{( 1 + 5 x ^{2} ) ^{\frac{3}{2}}}

\frac{d}{d x} (3 x^{\frac{2}{3}} - 3)

(x - 5) y^{^{'}} + y = x^{2} - 17

\int 2 a x + 1 d x

\int \frac{y}{4 + y ^{2}} d y

\int \frac{2}{x ( 3 x - 8 )} d x

What is the derivative of (i+xj+2xk/(sqrt(5x^2+1))) ?
The derivative of (i+xj+2xk/(sqrt(5x^2+1))) is (j+2k)/((1+5x^2)^{3/2)}-i(5x)/((1+5x^2)^{3/2)}
What is the first derivative of (i+xj+2xk/(sqrt(5x^2+1))) ?
The first derivative of (i+xj+2xk/(sqrt(5x^2+1))) is (j+2k)/((1+5x^2)^{3/2)}-i(5x)/((1+5x^2)^{3/2)}