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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Graph

Popular Examples

integral from 1 to 2 of (13)/(x^3+5x)

\int_{1}^{2} \frac{13}{x ^{3} + 5 x} d x

integral of 12-3x^2

\int 12 - 3 x^{2} d x

integral of (3-2t+t^2)

\int (3 - 2 t + t^{2}) d t

integral of (sin(x))/(5+cos(x))

\int \frac{sin ( x )}{5 + cos ( x )} d x

(\partial)/(\partial x)(x^2-xyz)

\frac{\partial}{\partial x} (x^{2} - x yz)

Frequently Asked Questions (FAQ)

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