What is the derivative of 10^{x^2-1} ?

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

What is the first derivative of 10^{x^2-1} ?

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

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derivative of

1 0^{x^{2} - 1}

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

Solution steps

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

Apply exponent rule:

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

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

= \frac{d}{d x} (e^{(x^{2} - 1) l n (10)})

Apply the chain rule:

e^{(x^{2} - 1) l n (10)} \frac{d}{d x} ((x^{2} - 1) ln (10))

= e^{(x^{2} - 1) l n (10)} \frac{d}{d x} ((x^{2} - 1) ln (10))

\frac{d}{d x} ((x^{2} - 1) ln (10)) = 2 ln (10) x

= e^{(x^{2} - 1) l n (10)} \cdot 2 ln (10) x

Simplify

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

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

\int w csc (4 w^{2} - 1) d w

x^{2} \frac{d ^{2} y}{d x ^{2}} = 0

\frac{d}{d x} (1.5 x - 0.25 x^{2})

cos (x)

\frac{d}{d x} (x e^{- x})

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