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Popular >

derivative of 5^{2x^3}

Solution

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

Solution

e^{x^{3} l n (25)} \cdot 6 ln (5) x^{2}

Solution steps

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

Simplify

5^{2 x^{3}} : 2 5^{x^{3}}

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

Apply exponent rule:

a^{b} = e^{b l n (a)}

2 5^{x^{3}} = e^{x^{3} l n (25)}

= \frac{d}{d x} (e^{x^{3} l n (25)})

Apply the chain rule:

e^{x^{3} l n (25)} \frac{d}{d x} (x^{3} ln (25))

= e^{x^{3} l n (25)} \frac{d}{d x} (x^{3} ln (25))

\frac{d}{d x} (x^{3} ln (25)) = 6 ln (5) x^{2}

= e^{x^{3} l n (25)} \cdot 6 ln (5) x^{2}

Popular Examples

xy^'=4x^2-2y,y(1)=3

x y^{^{'}} = 4 x^{2} - 2 y, y (1) = 3

area y^2-27x=0,x+y=0 area

y^{2} - 27 x = 0, x + y = 0

tangent of f(x)=x^3+4x-2,\at x=1 tangent of

f (x) = x^{3} + 4 x - 2, at x = 1

derivative of (x^{n+1}/(n+1))

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derivative of 50ln(2x+1)-x/2 derivative of

50 ln (2 x + 1) - \frac{x}{2}

Frequently Asked Questions (FAQ)

What is the derivative of 5^{2x^3} ?
The derivative of 5^{2x^3} is e^{x^3ln(25)}*6ln(5)x^2
What is the first derivative of 5^{2x^3} ?
The first derivative of 5^{2x^3} is e^{x^3ln(25)}*6ln(5)x^2