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Popular >

derivative of (x^3/(cos(x)))

Solution

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

Solution

3 x^{2} sec (x) + sec (x) tan (x) x^{3}

Solution steps

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

Simplify

\frac{x ^{3}}{cos ( x )} : x^{3} sec (x)

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

Apply the Product Rule:

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

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

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

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

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

= 3 x^{2} sec (x) + sec (x) tan (x) x^{3}

Popular Examples

inverse oflaplace (e^{(-2s)})/s inverse laplace

\frac{e ^{(- 2 s)}}{s}

integral of 1/(25e^{-7x)+e^{7x}}

\int \frac{1}{25 e ^{- 7 x} + e ^{7 x}} d x

(\partial ^2)/(\partial x\partial y)(ln(x^2+y^3))

\frac{\partial ^{2}}{\partial x \partial y} (ln (x^{2} + y^{3}))

y^{''}+36y=0,y(0)=0,y^'(0)=1

y^{^{''}} + 36 y = 0, y (0) = 0, y^{^{'}} (0) = 1

derivative of 2-3x derivative of

2 - 3 x

Frequently Asked Questions (FAQ)

What is the derivative of (x^3/(cos(x))) ?
The derivative of (x^3/(cos(x))) is 3x^2sec(x)+sec(x)tan(x)x^3
What is the first derivative of (x^3/(cos(x))) ?
The first derivative of (x^3/(cos(x))) is 3x^2sec(x)+sec(x)tan(x)x^3