What is the derivative of (2x-3x^3tan(x)) ?

The derivative of (2x-3x^3tan(x)) is (2-9x^2)tan(x)+sec^2(x)(2x-3x^3)

What is the first derivative of (2x-3x^3tan(x)) ?

The first derivative of (2x-3x^3tan(x)) is (2-9x^2)tan(x)+sec^2(x)(2x-3x^3)

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\frac{d}{d x} ((2 x - 3 x^{3}) tan (x))

(2 - 9 x^{2}) tan (x) + sec^{2} (x) (2 x - 3 x^{3})

Solution steps

\frac{d}{d x} ((2 x - 3 x^{3}) tan (x))

Apply the Product Rule:

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

f = 2 x - 3 x^{3}, g = tan (x)

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

\frac{d}{d x} (2 x - 3 x^{3}) = 2 - 9 x^{2}

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

= (2 - 9 x^{2}) tan (x) + sec^{2} (x) (2 x - 3 x^{3})

\frac{d}{d x} (arcsin (e^{- x}))

y = ln (x), x = e, y = 0

x \to - 9 lim (1 - 4 x^{3})

\int_{0}^{5} 2 e^{x} d x

x \to 2 lim (3 x^{3} + 5 x)

What is the derivative of (2x-3x^3tan(x)) ?
The derivative of (2x-3x^3tan(x)) is (2-9x^2)tan(x)+sec^2(x)(2x-3x^3)
What is the first derivative of (2x-3x^3tan(x)) ?
The first derivative of (2x-3x^3tan(x)) is (2-9x^2)tan(x)+sec^2(x)(2x-3x^3)