What is the derivative of f(x)=2*7^{2x^2+3} ?

The derivative of f(x)=2*7^{2x^2+3} is 8ln(7)*7^{2x^2+3}x

What is the first derivative of f(x)=2*7^{2x^2+3} ?

The first derivative of f(x)=2*7^{2x^2+3} is 8ln(7)*7^{2x^2+3}x

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derivative of

f (x) = 2 \cdot 7^{2 x^{2} + 3}

8 ln (7) \cdot 7^{2 x^{2} + 3} x

Solution steps

\frac{d}{d x} (2 \cdot 7^{2 x^{2} + 3})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (7^{2 x^{2} + 3})

Apply exponent rule:

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

7^{2 x^{2} + 3} = e^{(2 x^{2} + 3) l n (7)}

= 2 \frac{d}{d x} (e^{(2 x^{2} + 3) l n (7)})

Apply the chain rule:

e^{(2 x^{2} + 3) l n (7)} \frac{d}{d x} ((2 x^{2} + 3) ln (7))

= e^{(2 x^{2} + 3) l n (7)} \frac{d}{d x} ((2 x^{2} + 3) ln (7))

\frac{d}{d x} ((2 x^{2} + 3) ln (7)) = 4 ln (7) x

= 2 e^{(2 x^{2} + 3) l n (7)} \cdot 4 ln (7) x

Simplify

2 e^{(2 x^{2} + 3) l n (7)} \cdot 4 ln (7) x : 8 ln (7) \cdot 7^{2 x^{2} + 3} x

= 8 ln (7) \cdot 7^{2 x^{2} + 3} x

\int \frac{( x ^{3} )}{x ^{2} + 25} d x

\frac{\partial}{\partial t} (s cos (t))

\frac{d}{d x} (x + y)

x - x^{3}, - 2

\frac{\partial}{\partial y} (3 x z^{2} e^{y^{2}})

What is the derivative of f(x)=2*7^{2x^2+3} ?
The derivative of f(x)=2*7^{2x^2+3} is 8ln(7)*7^{2x^2+3}x
What is the first derivative of f(x)=2*7^{2x^2+3} ?
The first derivative of f(x)=2*7^{2x^2+3} is 8ln(7)*7^{2x^2+3}x