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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

y = arctan (\frac{x}{4}), (4, \frac{π}{4})

\frac{\partial}{\partial x} (x^{5} y)

\int \frac{4 x ^{2} + 2 x + 8}{x ( x ^{2} + 2 ) ^{2}} d x

x \to + 1 lim (- \frac{3}{x - 1})

x, at x = 25

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