Find derivatives of the functions defined as follows: y=3*4^{x^{2}+2}

Dottie Parra

Dottie Parra

Answered question

2021-10-08

Find derivatives of the functions defined as follows: y=34x2+2

Answer & Explanation

Roosevelt Houghton

Roosevelt Houghton

Skilled2021-10-09Added 106 answers

Step 1
To find the derivative of: y=34x2+2
Solution:
y=34x2+2
On differentiating both sides w.r.t x we get:
ddx(y)=ddx(34x2+2)
dydx=3(4x2+2)ln(4)ddx(x2+2) (using, ddx(f(g(x)))=f(g(x))g(x))
dydx=3(4x2+2)ln(4)(2x) (using, ddx(ax)=axlna,ddx(xn)=nxn1)
dydx=6x(4x2+2ln(4))
Step 2
Result:
dydx=6x(4x2+2ln(4))

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