What is the derivative of x^2tan(2x^5) ?

The derivative of x^2tan(2x^5) is 2xtan(2x^5)+10x^6sec^2(2x^5)

What is the first derivative of x^2tan(2x^5) ?

The first derivative of x^2tan(2x^5) is 2xtan(2x^5)+10x^6sec^2(2x^5)

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\frac{d}{d x} (x^{2} tan (2 x^{5}))

2 x tan (2 x^{5}) + 10 x^{6} sec^{2} (2 x^{5})

Solution steps

\frac{d}{d x} (x^{2} tan (2 x^{5}))

Apply the Product Rule:

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

f = x^{2}, g = tan (2 x^{5})

= \frac{d}{d x} (x^{2}) tan (2 x^{5}) + \frac{d}{d x} (tan (2 x^{5})) x^{2}

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

\frac{d}{d x} (tan (2 x^{5})) = sec^{2} (2 x^{5}) \cdot 10 x^{4}

= 2 x tan (2 x^{5}) + sec^{2} (2 x^{5}) \cdot 10 x^{4} x^{2}

sec^{2} (2 x^{5}) \cdot 10 x^{4} x^{2} = 10 x^{6} sec^{2} (2 x^{5})

= 2 x tan (2 x^{5}) + 10 x^{6} sec^{2} (2 x^{5})

What is the derivative of x^2tan(2x^5) ?
The derivative of x^2tan(2x^5) is 2xtan(2x^5)+10x^6sec^2(2x^5)
What is the first derivative of x^2tan(2x^5) ?
The first derivative of x^2tan(2x^5) is 2xtan(2x^5)+10x^6sec^2(2x^5)