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Popular >

derivative of sec^3(2x)

Solution

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

Solution

6 sec^{3} (2 x) tan (2 x)

Solution steps

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

Apply the chain rule:

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

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

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

= 3 (sec (2 x))^{2} sec (2 x) tan (2 x) \cdot 2

Simplify

3 sec^{2} (2 x) sec (2 x) tan (2 x) \cdot 2 : 6 sec^{3} (2 x) tan (2 x)

= 6 sec^{3} (2 x) tan (2 x)

Popular Examples

integral from-7 to-5 of 3/((x+6)^{8/11)}

\int_{- 7}^{- 5} \frac{3}{( x + 6 ) ^{\frac{8}{11}}} d x

tangent of f(x)=1-tan(x),\at x=-pi/4 tangent of

f (x) = 1 - tan (x), at x = - \frac{π}{4}

integral of 7e^{2x}

\int 7 e^{2 x} d x

(dy)/(dx)=((y-1))/(y+x)

\frac{d y}{d x} = \frac{( y - 1 )}{y + x}

inverse oflaplace ((s-1))/(s*(s^2+s+1))inverse laplace

\frac{( s - 1 )}{s \cdot ( s ^{2} + s + 1 )}

Frequently Asked Questions (FAQ)

What is the derivative of sec^3(2x) ?
The derivative of sec^3(2x) is 6sec^3(2x)tan(2x)
What is the first derivative of sec^3(2x) ?
The first derivative of sec^3(2x) is 6sec^3(2x)tan(2x)