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Popular >

derivative of f(x)=tan(x)sin(6x^3)

Solution

derivative of

f (x) = tan (x) sin (6 x^{3})

Solution

sec^{2} (x) sin (6 x^{3}) + cos (6 x^{3}) \cdot 18 x^{2} tan (x)

Solution steps

\frac{d}{d x} (tan (x) sin (6 x^{3}))

Apply the Product Rule:

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

f = tan (x), g = sin (6 x^{3})

= \frac{d}{d x} (tan (x)) sin (6 x^{3}) + \frac{d}{d x} (sin (6 x^{3})) tan (x)

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

\frac{d}{d x} (sin (6 x^{3})) = cos (6 x^{3}) \cdot 18 x^{2}

= sec^{2} (x) sin (6 x^{3}) + cos (6 x^{3}) \cdot 18 x^{2} tan (x)

Popular Examples

derivative of 10^x-10^{-x}

\frac{d}{d x} (1 0^{x} - 1 0^{- x})

derivative of f(x)=(x^2-2/x)^{-5}derivative of

f (x) = (x^{2} - \frac{2}{x})^{- 5}

limit as x approaches infinity of 13x(e^{1/x})-13x

x \to \infty lim (13 x (e^{\frac{1}{x}}) - 13 x)

y^'=8-y/(200)4,y(0)=50

y^{^{'}} = 8 - \frac{y}{200} 4, y (0) = 50

limit as x approaches pi/4 of sin(2x)

x \to \frac{π}{4} lim (sin (2 x))

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=tan(x)sin(6x^3) ?
The derivative of f(x)=tan(x)sin(6x^3) is sec^2(x)sin(6x^3)+cos(6x^3)*18x^2tan(x)
What is the first derivative of f(x)=tan(x)sin(6x^3) ?
The first derivative of f(x)=tan(x)sin(6x^3) is sec^2(x)sin(6x^3)+cos(6x^3)*18x^2tan(x)