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Popular >

derivative of tan(xsin(x))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = tan (x), g = sin (x)

= \frac{d}{d x} (tan (x)) sin (x) + \frac{d}{d x} (sin (x)) tan (x)

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

\frac{d}{d x} (sin (x)) = cos (x)

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

Simplify

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

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

Popular Examples

derivative of 4xe^x derivative of

4 x e^{x}

(\partial)/(\partial y)(4x^2+y^2-800)

\frac{\partial}{\partial y} (4 x^{2} + y^{2} - 800)

tangent of f(x)=x^3-8x^2,\at x=0 tangent of

f (x) = x^{3} - 8 x^{2}, at x = 0

integral of sec^6(x)tan^5(x)

\int sec^{6} (x) tan^{5} (x) d x

limit as x approaches 0 of (x^2)/2

x \to 0 lim (\frac{x ^{2}}{2})

Frequently Asked Questions (FAQ)

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