What is the derivative of sin((x^2-1/(sqrt(x)))) ?

The derivative of sin((x^2-1/(sqrt(x)))) is (cos(\frac{x^2-1)/(sqrt(x)))(3x^2+1)}{2xsqrt(x)}

What is the first derivative of sin((x^2-1/(sqrt(x)))) ?

The first derivative of sin((x^2-1/(sqrt(x)))) is (cos(\frac{x^2-1)/(sqrt(x)))(3x^2+1)}{2xsqrt(x)}

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\frac{d}{d x} (sin (\frac{x ^{2} - 1}{x}))

\frac{cos ( \frac{x ^{2} - 1}{x} ) ( 3 x ^{2} + 1 )}{2 x x}

Solution steps

\frac{d}{d x} (sin (\frac{x ^{2} - 1}{x}))

Apply the chain rule:

cos (\frac{x ^{2} - 1}{x}) \frac{d}{d x} (\frac{x ^{2} - 1}{x})

= cos (\frac{x ^{2} - 1}{x}) \frac{d}{d x} (\frac{x ^{2} - 1}{x})

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

= cos (\frac{x ^{2} - 1}{x}) \frac{3 x ^{2} + 1}{2 x x}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{cos ( \frac{x ^{2} - 1}{x} ) ( 3 x ^{2} + 1 )}{2 x x}

\frac{\partial}{\partial x} (e^{2 x} cos (6 y))

\frac{d}{d x} (sin^{3} (cos (x)))

\frac{d ^{2} y}{d x ^{2}} = \frac{( 6 x ^{5} )}{5} - 3 x

n \to \infty lim (n 0.25 - \frac{n}{n})

y = \frac{x ^{2} + 1}{x + 1}

What is the derivative of sin((x^2-1/(sqrt(x)))) ?
The derivative of sin((x^2-1/(sqrt(x)))) is (cos(\frac{x^2-1)/(sqrt(x)))(3x^2+1)}{2xsqrt(x)}
What is the first derivative of sin((x^2-1/(sqrt(x)))) ?
The first derivative of sin((x^2-1/(sqrt(x)))) is (cos(\frac{x^2-1)/(sqrt(x)))(3x^2+1)}{2xsqrt(x)}