What is the derivative of y=5^{4x^2+3x} ?

The derivative of y=5^{4x^2+3x} is ln(5)*5^{4x^2+3x}(8x+3)

What is the first derivative of y=5^{4x^2+3x} ?

The first derivative of y=5^{4x^2+3x} is ln(5)*5^{4x^2+3x}(8x+3)

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derivative of

y = 5^{4 x^{2} + 3 x}

ln (5) \cdot 5^{4 x^{2} + 3 x} (8 x + 3)

Solution steps

\frac{d}{d x} (5^{4 x^{2} + 3 x})

Apply exponent rule:

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

5^{4 x^{2} + 3 x} = e^{(4 x^{2} + 3 x) l n (5)}

= \frac{d}{d x} (e^{(4 x^{2} + 3 x) l n (5)})

Apply the chain rule:

e^{(4 x^{2} + 3 x) l n (5)} \frac{d}{d x} ((4 x^{2} + 3 x) ln (5))

= e^{(4 x^{2} + 3 x) l n (5)} \frac{d}{d x} ((4 x^{2} + 3 x) ln (5))

\frac{d}{d x} ((4 x^{2} + 3 x) ln (5)) = ln (5) (8 x + 3)

= e^{(4 x^{2} + 3 x) l n (5)} ln (5) (8 x + 3)

e^{(4 x^{2} + 3 x) l n (5)} = 5^{4 x^{2} + 3 x}

= ln (5) \cdot 5^{4 x^{2} + 3 x} (8 x + 3)

9 x y^{2}

\frac{d}{d t} (ln (t + 1))

f (x) = \frac{2 x}{x + 2}, at x = 2

x y y^{^{'}} = 1 - x^{2}

\int \frac{1}{( x ^{2} - 64 ) ^{\frac{3}{2}}} d x

What is the derivative of y=5^{4x^2+3x} ?
The derivative of y=5^{4x^2+3x} is ln(5)*5^{4x^2+3x}(8x+3)
What is the first derivative of y=5^{4x^2+3x} ?
The first derivative of y=5^{4x^2+3x} is ln(5)*5^{4x^2+3x}(8x+3)