What is the derivative of 4x^3arcsec(x) ?

The derivative of 4x^3arcsec(x) is 4(3x^2arcsec(x)+(x^2)/(sqrt(x^2-1)))

What is the first derivative of 4x^3arcsec(x) ?

The first derivative of 4x^3arcsec(x) is 4(3x^2arcsec(x)+(x^2)/(sqrt(x^2-1)))

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\frac{d}{d x} (4 x^{3} arcsec (x))

4 (3 x^{2} arcsec (x) + \frac{x ^{2}}{x ^{2} - 1})

Solution steps

\frac{d}{d x} (4 x^{3} arcsec (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (x^{3} arcsec (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3}, g = arcsec (x)

= 4 (\frac{d}{d x} (x^{3}) arcsec (x) + \frac{d}{d x} (arcsec (x)) x^{3})

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

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

= 4 (3 x^{2} arcsec (x) + \frac{1}{x x ^{2} - 1} x^{3})

\frac{1}{x x ^{2} - 1} x^{3} = \frac{x ^{2}}{x ^{2} - 1}

= 4 (3 x^{2} arcsec (x) + \frac{x ^{2}}{x ^{2} - 1})

\int 90 x^{2} sin (2 + 6 x^{3}) d x

1 - y^{2} d x - 1 - x^{2} d y = 0

f (x) = cos (\frac{x}{3})

f (x) = x^{7} + 10

ln (x) 5

What is the derivative of 4x^3arcsec(x) ?
The derivative of 4x^3arcsec(x) is 4(3x^2arcsec(x)+(x^2)/(sqrt(x^2-1)))
What is the first derivative of 4x^3arcsec(x) ?
The first derivative of 4x^3arcsec(x) is 4(3x^2arcsec(x)+(x^2)/(sqrt(x^2-1)))