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Popular >

derivative of 2(3x^2ln(10x)+x^2)

Solution

derivative of

2 (3 x^{2} ln (10 x) + x^{2})

Solution

2 (6 x ln (10 x) + 5 x)

Solution steps

\frac{d}{d x} (2 (3 x^{2} ln (10 x) + x^{2}))

Take the constant out:

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

= 2 \frac{d}{d x} (3 x^{2} ln (10 x) + x^{2})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 2 (\frac{d}{d x} (3 x^{2} ln (10 x)) + \frac{d}{d x} (x^{2}))

\frac{d}{d x} (3 x^{2} ln (10 x)) = 3 (2 x ln (10 x) + x)

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

= 2 (3 (2 x ln (10 x) + x) + 2 x)

Expand

3 (2 x ln (10 x) + x) + 2 x : 6 x ln (10 x) + 5 x

= 2 (6 x ln (10 x) + 5 x)

Popular Examples

integral of (-x^3-8x+5)

\int (- x^{3} - 8 x + 5) d x

integral from 0 to 2pi of 5x^2sin(1/4 x)

\int_{0}^{2 π} 5 x^{2} sin (\frac{1}{4} x) d x

derivative of 1/3 xsqrt(x^2+5)

\frac{d}{d x} (\frac{1}{3} x x^{2} + 5)

integral of 1/(sqrt(-4t^2+12t+7))

\int \frac{1}{- 4 t ^{2} + 12 t + 7} d t

integral from 0 to sqrt(pi of)sin(x^2)

\int_{0}^{π} sin (x^{2}) d x

Frequently Asked Questions (FAQ)

What is the derivative of 2(3x^2ln(10x)+x^2) ?
The derivative of 2(3x^2ln(10x)+x^2) is 2(6xln(10x)+5x)
What is the first derivative of 2(3x^2ln(10x)+x^2) ?
The first derivative of 2(3x^2ln(10x)+x^2) is 2(6xln(10x)+5x)