What is the derivative of (4x^2tan(x)/(sec(x))) ?

The derivative of (4x^2tan(x)/(sec(x))) is 4(x^2cos(x)+2xsin(x))

What is the first derivative of (4x^2tan(x)/(sec(x))) ?

The first derivative of (4x^2tan(x)/(sec(x))) is 4(x^2cos(x)+2xsin(x))

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\frac{d}{d x} (\frac{4 x ^{2} tan ( x )}{sec ( x )})

4 (x^{2} cos (x) + 2 x sin (x))

Solution steps

\frac{d}{d x} (\frac{4 x ^{2} tan ( x )}{sec ( x )})

Simplify

\frac{4 x ^{2} tan ( x )}{sec ( x )} : 4 x^{2} tan (x) cos (x)

= \frac{d}{d x} (4 x^{2} tan (x) cos (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (x^{2} tan (x) cos (x))

Apply the Product Rule:

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

f = x^{2}, g = tan (x) cos (x)

= 4 (\frac{d}{d x} (x^{2}) tan (x) cos (x) + \frac{d}{d x} (tan (x) cos (x)) x^{2})

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

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

= 4 (2 x tan (x) cos (x) + cos (x) x^{2})

cos (x) tan (x) = sin (x)

= 4 (x^{2} cos (x) + 2 x sin (x))

\frac{d}{d x} (x^{8} (x - 1)^{7})

\int (2 x - 4) d x

\int (- \frac{3}{7} x^{5} + \frac{1}{5} x^{3} - \frac{7}{4} x^{2}) d x

\int \frac{3 x}{x ^{2} + 2 x - 8} d x

\frac{d}{d x} (6 x + 3)

What is the derivative of (4x^2tan(x)/(sec(x))) ?
The derivative of (4x^2tan(x)/(sec(x))) is 4(x^2cos(x)+2xsin(x))
What is the first derivative of (4x^2tan(x)/(sec(x))) ?
The first derivative of (4x^2tan(x)/(sec(x))) is 4(x^2cos(x)+2xsin(x))