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Popular >

derivative of sec^3(sqrt(x))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

sum from n=1 to infinity of (ln(3))^n

n = 1 \sum \infty (ln (3))^{n}

tangent of f(x)=sqrt(7x+11),(2,5)tangent of

f (x) = 7 x + 11, (2, 5)

y^{''}-4y=e^xcos(x),y(0)=0.7,y^'(0)=-1.5

y^{^{''}} - 4 y = e^{x} cos (x), y (0) = 0.7, y^{^{'}} (0) = - 1.5

\frac{d y}{d t} = y^{2}

derivative of f(x)=ln(6x)derivative of

f (x) = ln (6 x)

Frequently Asked Questions (FAQ)

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