What is the derivative of (x^3+2/(cos(x))) ?

The derivative of (x^3+2/(cos(x))) is (3x^2cos(x)+sin(x)(x^3+2))/(cos^2(x))

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

The first derivative of (x^3+2/(cos(x))) is (3x^2cos(x)+sin(x)(x^3+2))/(cos^2(x))

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d}{d x} (cos (x)) = - sin (x)

= \frac{3 x ^{2} cos ( x ) - ( - sin ( x ) ) ( x ^{3} + 2 )}{( cos ( x ) ) ^{2}}

Simplify

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

\frac{d}{d x} (arcsin (x^{3} y))

\int e^{2 x} d x

\int_{1}^{e^{2}} \frac{3}{x} d x

\int \frac{1}{( 2 x + 5 ) ^{2}} d x

\int \frac{1}{x ^{2} ( x - 1 ) ( x - 2 )} d x

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