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Popular >

derivative of f(x)=tan^2(3e^x)

Solution

derivative of

f (x) = tan^{2} (3 e^{x})

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

Popular Examples

derivative of 7/((2x+1)^2)derivative of

\frac{7}{( 2 x + 1 ) ^{2}}

x^{''}=-x+0.1x^'

x^{^{''}} = - x + 0.1 x^{^{'}}

(y^{''}+10y^'+149)/(4y)=0

\frac{y ^{^{''}} + 10 y ^{^{'}} + 149}{4 y} = 0

limit as x approaches 2 of+f(x)

x \to 2 lim (+ f (x))

integral of (2x-3)/(x^2+10x+29)

\int \frac{2 x - 3}{x ^{2} + 10 x + 29} d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=tan^2(3e^x) ?
The derivative of f(x)=tan^2(3e^x) is 6e^xsec^2(3e^x)tan(3e^x)
What is the first derivative of f(x)=tan^2(3e^x) ?
The first derivative of f(x)=tan^2(3e^x) is 6e^xsec^2(3e^x)tan(3e^x)