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

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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}

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