What is the derivative of 6x^{3/2}sec(x) ?

The derivative of 6x^{3/2}sec(x) is 6((3x^{1/2}sec(x))/2+x^{3/2}sec(x)tan(x))

What is the first derivative of 6x^{3/2}sec(x) ?

The first derivative of 6x^{3/2}sec(x) is 6((3x^{1/2}sec(x))/2+x^{3/2}sec(x)tan(x))

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\frac{d}{d x} (6 x^{\frac{3}{2}} sec (x))

6 (\frac{3 x ^{\frac{1}{2}} sec ( x )}{2} + x^{\frac{3}{2}} sec (x) tan (x))

Solution steps

\frac{d}{d x} (6 x^{\frac{3}{2}} sec (x))

Take the constant out:

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

= 6 \frac{d}{d x} (x^{\frac{3}{2}} sec (x))

Apply the Product Rule:

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

f = x^{\frac{3}{2}}, g = sec (x)

= 6 (\frac{d}{d x} (x^{\frac{3}{2}}) sec (x) + \frac{d}{d x} (sec (x)) x^{\frac{3}{2}})

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

\frac{d}{d x} (sec (x)) = sec (x) tan (x)

= 6 (\frac{3 x ^{\frac{1}{2}}}{2} sec (x) + sec (x) tan (x) x^{\frac{3}{2}})

Multiply fractions:

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

= 6 (\frac{3 x ^{\frac{1}{2}} sec ( x )}{2} + x^{\frac{3}{2}} sec (x) tan (x))

x^{2} y^{^{''}} - x y^{^{'}} + y = 0, y = x

\frac{d}{d x} (- 0.4 x^{2} + 2.2 x + 4.7)

\frac{d}{d x} (e^{x} (tan (x) - x))

x \to 0 lim (\frac{x}{x + 1})

2 x^{3} + 3 x^{2} - 12 x + 2

What is the derivative of 6x^{3/2}sec(x) ?
The derivative of 6x^{3/2}sec(x) is 6((3x^{1/2}sec(x))/2+x^{3/2}sec(x)tan(x))
What is the first derivative of 6x^{3/2}sec(x) ?
The first derivative of 6x^{3/2}sec(x) is 6((3x^{1/2}sec(x))/2+x^{3/2}sec(x)tan(x))