What is the derivative of f(x)=x^4sqrt(sec(5x)) ?

The derivative of f(x)=x^4sqrt(sec(5x)) is 4x^3sqrt(sec(5x))+(5x^4tan(5x)sqrt(sec(5x)))/2

What is the first derivative of f(x)=x^4sqrt(sec(5x)) ?

The first derivative of f(x)=x^4sqrt(sec(5x)) is 4x^3sqrt(sec(5x))+(5x^4tan(5x)sqrt(sec(5x)))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = x^{4} sec (5 x)

4 x^{3} sec (5 x) + \frac{5 x ^{4} tan ( 5 x ) sec ( 5 x )}{2}

Solution steps

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

Apply the Product Rule:

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

f = x^{4}, g = sec (5 x)

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

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

\frac{d}{d x} (sec (5 x)) = \frac{5 tan ( 5 x ) sec ( 5 x )}{2}

= 4 x^{3} sec (5 x) + \frac{5 tan ( 5 x ) sec ( 5 x )}{2} x^{4}

Multiply fractions:

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

= 4 x^{3} sec (5 x) + \frac{5 x ^{4} tan ( 5 x ) sec ( 5 x )}{2}

\frac{\partial}{\partial x} (sin (x^{2}) y)

\int_{2}^{\infty} e^{- 5 x} d x

\int 7 ln (x^{2} - x + 2) d x

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

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

What is the derivative of f(x)=x^4sqrt(sec(5x)) ?
The derivative of f(x)=x^4sqrt(sec(5x)) is 4x^3sqrt(sec(5x))+(5x^4tan(5x)sqrt(sec(5x)))/2
What is the first derivative of f(x)=x^4sqrt(sec(5x)) ?
The first derivative of f(x)=x^4sqrt(sec(5x)) is 4x^3sqrt(sec(5x))+(5x^4tan(5x)sqrt(sec(5x)))/2