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Popular >

derivative of 10x^3tan(x)

Solution

\frac{d}{d x} (10 x^{3} tan (x))

Solution

10 (3 x^{2} tan (x) + sec^{2} (x) x^{3})

Solution steps

\frac{d}{d x} (10 x^{3} tan (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 10 \frac{d}{d x} (x^{3} tan (x))

Apply the Product Rule:

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

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

= 10 (\frac{d}{d x} (x^{3}) tan (x) + \frac{d}{d x} (tan (x)) x^{3})

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

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

= 10 (3 x^{2} tan (x) + sec^{2} (x) x^{3})

Popular Examples

limit as x approaches 5 of sqrt(x^2-9)

x \to 5 lim (x^{2} - 9)

(dy)/(dx)=7xsqrt(5y+3)

\frac{d y}{d x} = 7 x 5 y + 3

derivative of (2000/(sin(3x)))

\frac{d}{d x} (\frac{2000}{sin ( 3 x )})

derivative of y=(5+xf(x))/(sqrt(x))derivative of

y = \frac{5 + x f ( x )}{x}

area y=1-x^2,y=2x,y= 1/2 x area

y = 1 - x^{2}, y = 2 x, y = \frac{1}{2} x

Frequently Asked Questions (FAQ)

What is the derivative of 10x^3tan(x) ?
The derivative of 10x^3tan(x) is 10(3x^2tan(x)+sec^2(x)x^3)
What is the first derivative of 10x^3tan(x) ?
The first derivative of 10x^3tan(x) is 10(3x^2tan(x)+sec^2(x)x^3)