What is the derivative of y=ln(x)sec^3(x) ?

The derivative of y=ln(x)sec^3(x) is (sec^3(x))/x+3sec^3(x)tan(x)ln(x)

What is the first derivative of y=ln(x)sec^3(x) ?

The first derivative of y=ln(x)sec^3(x) is (sec^3(x))/x+3sec^3(x)tan(x)ln(x)

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derivative of

y = ln (x) sec^{3} (x)

\frac{sec ^{3} ( x )}{x} + 3 sec^{3} (x) tan (x) ln (x)

Solution steps

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

Apply the Product Rule:

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

f = ln (x), g = sec^{3} (x)

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

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

= \frac{1}{x} sec^{3} (x) + 3 sec^{3} (x) tan (x) ln (x)

\frac{1}{x} sec^{3} (x) = \frac{sec ^{3} ( x )}{x}

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

(x + 2)^{4}

\frac{d}{d t} (15 + 300 t)

\frac{1}{l}

x^{9} - 10 x^{5} + 2 x^{2} - 10

\frac{y}{( x - y ) 2}

What is the derivative of y=ln(x)sec^3(x) ?
The derivative of y=ln(x)sec^3(x) is (sec^3(x))/x+3sec^3(x)tan(x)ln(x)
What is the first derivative of y=ln(x)sec^3(x) ?
The first derivative of y=ln(x)sec^3(x) is (sec^3(x))/x+3sec^3(x)tan(x)ln(x)