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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

(t - 3)^{3}

\int_{0}^{2} \frac{x}{( 1 + 2 x ^{2} ) ^{2}} d x

\int_{- 18}^{32} \frac{1}{2 x} d x

\frac{d ^{2}}{d x ^{2}} (x^{2} + 11)

\int_{0}^{1} x^{2} e^{x^{3} + 0} d x

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