What is the derivative of 10^{x^2} ?

The derivative of 10^{x^2} is ln(10)*5^{x^2}*2^{x^2+1}x

What is the first derivative of 10^{x^2} ?

The first derivative of 10^{x^2} is ln(10)*5^{x^2}*2^{x^2+1}x

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\frac{d}{d x} (1 0^{x^{2}})

ln (10) \cdot 5^{x^{2}} \cdot 2^{x^{2} + 1} x

Solution steps

\frac{d}{d x} (1 0^{x^{2}})

Apply exponent rule:

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

1 0^{x^{2}} = e^{x^{2} l n (10)}

= \frac{d}{d x} (e^{x^{2} l n (10)})

Apply the chain rule:

e^{x^{2} l n (10)} \frac{d}{d x} (x^{2} ln (10))

= e^{x^{2} l n (10)} \frac{d}{d x} (x^{2} ln (10))

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

= e^{x^{2} l n (10)} \cdot 2 ln (10) x

Simplify

e^{x^{2} l n (10)} \cdot 2 ln (10) x : ln (10) \cdot 5^{x^{2}} \cdot 2^{x^{2} + 1} x

= ln (10) \cdot 5^{x^{2}} \cdot 2^{x^{2} + 1} x

\int_{0}^{4} \frac{1}{9 + x ^{2}} d x

\frac{\partial}{\partial x} (- 6 x + 12)

y^{2} = 4 x, y = 4 x - 2

y = \frac{1}{x}, x = a

\frac{a}{y ^{10}}

What is the derivative of 10^{x^2} ?
The derivative of 10^{x^2} is ln(10)*5^{x^2}*2^{x^2+1}x
What is the first derivative of 10^{x^2} ?
The first derivative of 10^{x^2} is ln(10)*5^{x^2}*2^{x^2+1}x