What is the derivative of sqrt(sec(x)*x^5) ?

The derivative of sqrt(sec(x)*x^5) is (x^5tan(x)sqrt(sec(x)))/2+5x^4sqrt(sec(x))

What is the first derivative of sqrt(sec(x)*x^5) ?

The first derivative of sqrt(sec(x)*x^5) is (x^5tan(x)sqrt(sec(x)))/2+5x^4sqrt(sec(x))

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\frac{d}{d x} (sec (x) \cdot x^{5})

\frac{x ^{5} tan ( x ) sec ( x )}{2} + 5 x^{4} sec (x)

Solution steps

\frac{d}{d x} (sec (x) x^{5})

Apply the Product Rule:

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

f = sec (x), g = x^{5}

= \frac{d}{d x} (sec (x)) x^{5} + \frac{d}{d x} (x^{5}) sec (x)

\frac{d}{d x} (sec (x)) = \frac{tan ( x ) sec ( x )}{2}

\frac{d}{d x} (x^{5}) = 5 x^{4}

= \frac{tan ( x ) sec ( x )}{2} x^{5} + 5 x^{4} sec (x)

Multiply fractions:

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

= \frac{x ^{5} tan ( x ) sec ( x )}{2} + 5 x^{4} sec (x)

\frac{\partial}{\partial x} (x + 2 y + z)

\int \frac{12 x + 30}{x ^{2} + 2 x - 8} d x

x \to 1 lim (e^{x^{2} + 7 x - 8})

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

\int_{- 2}^{4} (x - 9) d x

What is the derivative of sqrt(sec(x)*x^5) ?
The derivative of sqrt(sec(x)*x^5) is (x^5tan(x)sqrt(sec(x)))/2+5x^4sqrt(sec(x))
What is the first derivative of sqrt(sec(x)*x^5) ?
The first derivative of sqrt(sec(x)*x^5) is (x^5tan(x)sqrt(sec(x)))/2+5x^4sqrt(sec(x))