What is the derivative of 7^{x^4+2x} ?

The derivative of 7^{x^4+2x} is ln(7)*7^{x^4+2x}(4x^3+2)

What is the first derivative of 7^{x^4+2x} ?

The first derivative of 7^{x^4+2x} is ln(7)*7^{x^4+2x}(4x^3+2)

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

ln (7) \cdot 7^{x^{4} + 2 x} (4 x^{3} + 2)

Solution steps

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

Apply exponent rule:

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

7^{x^{4} + 2 x} = e^{(x^{4} + 2 x) l n (7)}

= \frac{d}{d x} (e^{(x^{4} + 2 x) l n (7)})

Apply the chain rule:

e^{(x^{4} + 2 x) l n (7)} \frac{d}{d x} ((x^{4} + 2 x) ln (7))

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

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

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

e^{(x^{4} + 2 x) l n (7)} = 7^{x^{4} + 2 x}

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

f (x) = 2 x^{4} - 16 x^{3} + 9

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

y = sin (2 x), at x = \frac{3 π}{4}

\int_{0}^{π} sin^{4} (x) d x

x^{2} y^{3} d x + x^{3} y^{2} d y = 0

What is the derivative of 7^{x^4+2x} ?
The derivative of 7^{x^4+2x} is ln(7)*7^{x^4+2x}(4x^3+2)
What is the first derivative of 7^{x^4+2x} ?
The first derivative of 7^{x^4+2x} is ln(7)*7^{x^4+2x}(4x^3+2)