What is the derivative of (5x^2tan(x)/(sec(x))) ?

The derivative of (5x^2tan(x)/(sec(x))) is 5(x^2cos(x)+2xsin(x))

What is the first derivative of (5x^2tan(x)/(sec(x))) ?

The first derivative of (5x^2tan(x)/(sec(x))) is 5(x^2cos(x)+2xsin(x))

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\frac{d}{d x} (\frac{5 x ^{2} tan ( x )}{sec ( x )})

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

Solution steps

\frac{d}{d x} (\frac{5 x ^{2} tan ( x )}{sec ( x )})

Simplify

\frac{5 x ^{2} tan ( x )}{sec ( x )} : 5 x^{2} tan (x) cos (x)

= \frac{d}{d x} (5 x^{2} tan (x) cos (x))

Take the constant out:

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

= 5 \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)

= 5 (\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)

= 5 (2 x tan (x) cos (x) + cos (x) x^{2})

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

= 5 (x^{2} cos (x) + 2 x sin (x))

\int_{0}^{1} (8 x^{2} - 5) e^{x} d x

\frac{\partial}{\partial y} (2 y t + x j)

\int \frac{x ^{2}}{16 + x ^{2}} d x

\int 4 t^{3} y - 15 t^{2} - y d t

11 x - 3, 10 x - 5, [12, 34]

What is the derivative of (5x^2tan(x)/(sec(x))) ?
The derivative of (5x^2tan(x)/(sec(x))) is 5(x^2cos(x)+2xsin(x))
What is the first derivative of (5x^2tan(x)/(sec(x))) ?
The first derivative of (5x^2tan(x)/(sec(x))) is 5(x^2cos(x)+2xsin(x))