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Popular >

derivative of sec^2(5x*5)

Solution

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

Solution

50 sec^{2} (5 x) tan (5 x)

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= 5 \cdot 2 sec (5 x) sec (5 x) tan (5 x) \cdot 5

Simplify

5 \cdot 2 sec (5 x) sec (5 x) tan (5 x) \cdot 5 : 50 sec^{2} (5 x) tan (5 x)

= 50 sec^{2} (5 x) tan (5 x)

Popular Examples

derivative of (arcsin(2x)/(arccos(2x)))

\frac{d}{d x} (\frac{arcsin ( 2 x )}{arccos ( 2 x )})

derivative of x^{1/(1-x})

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

ty^'-2y=t^3e^{-t}

t y^{^{'}} - 2 y = t^{3} e^{- t}

integral from 0 to 8 of sqrt(1+36x)

\int_{0}^{8} 1 + 36 x d x

tangent of f(x)=2x^2+4x,\at x=-2 tangent of

f (x) = 2 x^{2} + 4 x, at x = - 2

Frequently Asked Questions (FAQ)

What is the derivative of sec^2(5x*5) ?
The derivative of sec^2(5x*5) is 50sec^2(5x)tan(5x)
What is the first derivative of sec^2(5x*5) ?
The first derivative of sec^2(5x*5) is 50sec^2(5x)tan(5x)