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Popular >

derivative of (-2x-3x^5tan(x))

Solution

\frac{d}{d x} ((- 2 x - 3 x^{5}) tan (x))

Solution

(- 2 - 15 x^{4}) tan (x) + sec^{2} (x) (- 2 x - 3 x^{5})

Solution steps

\frac{d}{d x} ((- 2 x - 3 x^{5}) tan (x))

Apply the Product Rule:

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

f = - 2 x - 3 x^{5}, g = tan (x)

= \frac{d}{d x} (- 2 x - 3 x^{5}) tan (x) + \frac{d}{d x} (tan (x)) (- 2 x - 3 x^{5})

\frac{d}{d x} (- 2 x - 3 x^{5}) = - 2 - 15 x^{4}

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

= (- 2 - 15 x^{4}) tan (x) + sec^{2} (x) (- 2 x - 3 x^{5})

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Frequently Asked Questions (FAQ)

What is the derivative of (-2x-3x^5tan(x)) ?
The derivative of (-2x-3x^5tan(x)) is (-2-15x^4)tan(x)+sec^2(x)(-2x-3x^5)
What is the first derivative of (-2x-3x^5tan(x)) ?
The first derivative of (-2x-3x^5tan(x)) is (-2-15x^4)tan(x)+sec^2(x)(-2x-3x^5)