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Popular >

derivative of tan(5x+1/(2x^2))

Solution

\frac{d}{d x} (tan (5 x) + \frac{1}{2 x ^{2}})

Solution

sec^{2} (5 x) \cdot 5 - \frac{1}{x ^{3}}

Solution steps

\frac{d}{d x} (tan (5 x) + \frac{1}{2 x ^{2}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (tan (5 x)) + \frac{d}{d x} (\frac{1}{2 x ^{2}})

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

\frac{d}{d x} (\frac{1}{2 x ^{2}}) = - \frac{1}{x ^{3}}

= sec^{2} (5 x) \cdot 5 - \frac{1}{x ^{3}}

Popular Examples

-3y^'+(3y)/x =x^4y^4

- 3 y^{^{'}} + \frac{3 y}{x} = x^{4} y^{4}

integral of 4/(2x-1)

\int \frac{4}{2 x - 1} d x

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\frac{d}{d x} (2 x e^{3 x})

limit as x approaches 6 of 3/(x-6)

x \to 6 lim (\frac{3}{x - 6})

derivative of ((x^5-5)/((x+1)))

\frac{d}{d x} (\frac{( x ^{5} - 5 )}{( x + 1 )})

Frequently Asked Questions (FAQ)

What is the derivative of tan(5x+1/(2x^2)) ?
The derivative of tan(5x+1/(2x^2)) is sec^2(5x)*5-1/(x^3)
What is the first derivative of tan(5x+1/(2x^2)) ?
The first derivative of tan(5x+1/(2x^2)) is sec^2(5x)*5-1/(x^3)