What is the derivative of 3x^2sin(xtan(x)) ?

The derivative of 3x^2sin(xtan(x)) is 3(2xsin(x)tan(x)+sin(x)(1+sec^2(x))x^2)

What is the first derivative of 3x^2sin(xtan(x)) ?

The first derivative of 3x^2sin(xtan(x)) is 3(2xsin(x)tan(x)+sin(x)(1+sec^2(x))x^2)

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

3 (2 x sin (x) tan (x) + sin (x) (1 + sec^{2} (x)) x^{2})

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = x^{2}, g = sin (x) tan (x)

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

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

\frac{d}{d x} (sin (x) tan (x)) = sin (x) (1 + sec^{2} (x))

= 3 (2 x sin (x) tan (x) + sin (x) (1 + sec^{2} (x)) x^{2})

What is the derivative of 3x^2sin(xtan(x)) ?
The derivative of 3x^2sin(xtan(x)) is 3(2xsin(x)tan(x)+sin(x)(1+sec^2(x))x^2)
What is the first derivative of 3x^2sin(xtan(x)) ?
The first derivative of 3x^2sin(xtan(x)) is 3(2xsin(x)tan(x)+sin(x)(1+sec^2(x))x^2)