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Popular >

derivative of tan^3(1+2x^2)

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

= 12 x tan^{2} (1 + 2 x^{2}) sec^{2} (1 + 2 x^{2})

Popular Examples

derivative of x(3x-9)^3 derivative of

x (3 x - 9)^{3}

integral of (x^2)/(sqrt(a^2+x^2))

\int \frac{x ^{2}}{a ^{2} + x ^{2}} d x

integral of (sin(x^3))

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

y^'(x)=((1+3x^2))/(3y^2-6y),y(0)=1

y^{^{'}} (x) = \frac{( 1 + 3 x ^{2} )}{3 y ^{2} - 6 y}, y (0) = 1

derivative of axcos(2x+bxsin(2x))

\frac{d}{d x} (a x cos (2 x) + b x sin (2 x))

Frequently Asked Questions (FAQ)

What is the derivative of tan^3(1+2x^2) ?
The derivative of tan^3(1+2x^2) is 12xtan^2(1+2x^2)sec^2(1+2x^2)
What is the first derivative of tan^3(1+2x^2) ?
The first derivative of tan^3(1+2x^2) is 12xtan^2(1+2x^2)sec^2(1+2x^2)