What is the derivative of x^3tan(x) ?

The derivative of x^3tan(x) is 3x^2tan(x)+sec^2(x)x^3

What is the first derivative of x^3tan(x) ?

The first derivative of x^3tan(x) is 3x^2tan(x)+sec^2(x)x^3

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

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

Solution steps

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

Apply the Product Rule:

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

f = x^{3}, g = tan (x)

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

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

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

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

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