What is the derivative of f(x)=(x^4)/(cos(x)) ?

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

What is the first derivative of f(x)=(x^4)/(cos(x)) ?

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

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derivative of

f (x) = \frac{x ^{4}}{cos ( x )}

4 x^{3} sec (x) + sec (x) tan (x) x^{4}

Solution steps

\frac{d}{d x} (\frac{x ^{4}}{cos ( x )})

Simplify

\frac{x ^{4}}{cos ( x )} : x^{4} sec (x)

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

Apply the Product Rule:

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

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

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

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

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

= 4 x^{3} sec (x) + sec (x) tan (x) x^{4}

\int x - (x^{2} - 2) d x

\int \frac{8 x ^{2} + 6}{( x - 5 ) ^{3}} d x

\frac{d}{d x} (arctan (x + 1) + 2 x - y)

y^{^{''}} + 25 y = cos (2 x)

\int \frac{( x + 7 ) ^{5}}{x} d x

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