What is the derivative of sqrt(sin(x-1(x^3))) ?

The derivative of sqrt(sin(x-1(x^3))) is (sqrt(x)(xcos(x-1)+3sin(x-1)))/(2sqrt(sin(x-1)))

What is the first derivative of sqrt(sin(x-1(x^3))) ?

The first derivative of sqrt(sin(x-1(x^3))) is (sqrt(x)(xcos(x-1)+3sin(x-1)))/(2sqrt(sin(x-1)))

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\frac{d}{d x} (sin (x - 1) (x^{3}))

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

Solution steps

\frac{d}{d x} (sin (x - 1) (x^{3}))

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is the derivative of sqrt(sin(x-1(x^3))) ?
The derivative of sqrt(sin(x-1(x^3))) is (sqrt(x)(xcos(x-1)+3sin(x-1)))/(2sqrt(sin(x-1)))
What is the first derivative of sqrt(sin(x-1(x^3))) ?
The first derivative of sqrt(sin(x-1(x^3))) is (sqrt(x)(xcos(x-1)+3sin(x-1)))/(2sqrt(sin(x-1)))