What is the derivative of tan(3x-x^2) ?

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

What is the first derivative of tan(3x-x^2) ?

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

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

sec^{2} (3 x - x^{2}) (3 - 2 x)

Solution steps

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

Apply the chain rule:

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

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

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

= sec^{2} (3 x - x^{2}) (3 - 2 x)

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