What is the derivative of xtan(3x^2+4x+1) ?

The derivative of xtan(3x^2+4x+1) is tan(3x^2+4x+1)+xsec^2(3x^2+4x+1)(6x+4)

What is the first derivative of xtan(3x^2+4x+1) ?

The first derivative of xtan(3x^2+4x+1) is tan(3x^2+4x+1)+xsec^2(3x^2+4x+1)(6x+4)

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derivative of

x tan (3 x^{2} + 4 x + 1)

tan (3 x^{2} + 4 x + 1) + x sec^{2} (3 x^{2} + 4 x + 1) (6 x + 4)

Solution steps

\frac{d}{d x} (x tan (3 x^{2} + 4 x + 1))

Apply the Product Rule:

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

f = x, g = tan (3 x^{2} + 4 x + 1)

= \frac{d x}{d x} tan (3 x^{2} + 4 x + 1) + \frac{d}{d x} (tan (3 x^{2} + 4 x + 1)) x

\frac{d x}{d x} = 1

\frac{d}{d x} (tan (3 x^{2} + 4 x + 1)) = sec^{2} (3 x^{2} + 4 x + 1) (6 x + 4)

= 1 \cdot tan (3 x^{2} + 4 x + 1) + sec^{2} (3 x^{2} + 4 x + 1) (6 x + 4) x

Simplify

= tan (3 x^{2} + 4 x + 1) + x sec^{2} (3 x^{2} + 4 x + 1) (6 x + 4)

What is the derivative of xtan(3x^2+4x+1) ?
The derivative of xtan(3x^2+4x+1) is tan(3x^2+4x+1)+xsec^2(3x^2+4x+1)(6x+4)
What is the first derivative of xtan(3x^2+4x+1) ?
The first derivative of xtan(3x^2+4x+1) is tan(3x^2+4x+1)+xsec^2(3x^2+4x+1)(6x+4)