What is the derivative of 10^{5x^2-3x} ?

The derivative of 10^{5x^2-3x} is ln(10)*10^{5x^2-3x}(10x-3)

What is the first derivative of 10^{5x^2-3x} ?

The first derivative of 10^{5x^2-3x} is ln(10)*10^{5x^2-3x}(10x-3)

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derivative of

1 0^{5 x^{2} - 3 x}

ln (10) \cdot 1 0^{5 x^{2} - 3 x} (10 x - 3)

Solution steps

\frac{d}{d x} (1 0^{5 x^{2} - 3 x})

Apply exponent rule:

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

1 0^{5 x^{2} - 3 x} = e^{(5 x^{2} - 3 x) l n (10)}

= \frac{d}{d x} (e^{(5 x^{2} - 3 x) l n (10)})

Apply the chain rule:

e^{(5 x^{2} - 3 x) l n (10)} \frac{d}{d x} ((5 x^{2} - 3 x) ln (10))

= e^{(5 x^{2} - 3 x) l n (10)} \frac{d}{d x} ((5 x^{2} - 3 x) ln (10))

\frac{d}{d x} ((5 x^{2} - 3 x) ln (10)) = ln (10) (10 x - 3)

= e^{(5 x^{2} - 3 x) l n (10)} ln (10) (10 x - 3)

e^{(5 x^{2} - 3 x) l n (10)} = 1 0^{5 x^{2} - 3 x}

= ln (10) \cdot 1 0^{5 x^{2} - 3 x} (10 x - 3)

\int_{1}^{\infty} e^{- x^{2}} d x

y = x^{2}, x = y + 2, - 1, 2

f (x) = \frac{1 + x}{e ^{x}}

\frac{d}{d x} (\frac{2 ab}{( a - b x ) ^{2}})

\frac{\partial}{\partial y} (2 x - 2 y)

What is the derivative of 10^{5x^2-3x} ?
The derivative of 10^{5x^2-3x} is ln(10)*10^{5x^2-3x}(10x-3)
What is the first derivative of 10^{5x^2-3x} ?
The first derivative of 10^{5x^2-3x} is ln(10)*10^{5x^2-3x}(10x-3)