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Popular >

derivative of x^2sin(x)tan(x)

Solution

derivative of

x^{2} sin (x) tan (x)

Solution

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

Solution steps

\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)

= \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))

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

Popular Examples

derivative of y= 1/27 (9x^2+6)^{3/2}derivative of

y = \frac{1}{27} (9 x^{2} + 6)^{\frac{3}{2}}

derivative of tan(2/x)

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

integral of (x-6)/(x^2-16x+65)

\int \frac{x - 6}{x ^{2} - 16 x + 65} d x

integral of y/((y+1))

\int \frac{y}{( y + 1 )} d y

integral of 2sin^3(x)cos(x)

\int 2 sin^{3} (x) cos (x) d x

Frequently Asked Questions (FAQ)

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